Efficiency and Sustainability in the Energy and Chemical Industries

Jakob de Swaan Arons Hedzer van der Kooi Delft University of Technology

Delft, The Netherlands

Kr is h nan San ka ranaray a n an ExxonMobil Research and Engineering

Fairfax, Virginia, U. S. A.

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Preface

For many of us the energy crisis of the 1970s and 1980s is still fresh in ourmemory. The crisis was of political origin, not a real shortage. The developedcountries responded by focusing on increasing energy efficiency, at home andin industry, and by taking initiatives to make them less dependent on liquidfossils from the Middle East. More than ever before, attention shifted to coalas an alternative energy resource—its exploration, production, transporta-tion, and marketing. Massive research and development programs wereinitiated to make available clean and efficient coal utilization and more easilyhandled materials as gaseous and liquid conversion products. Obviously,large multinational oil companies played an important role in these initia-tives, as they considered energy, not oil, their ultimate business.

At the same time there was growing concern worldwide for the envi-ronment. With the industrial society proceeding at full speed with massproduction and consumption, the world became aware that this was accom-panied by mass emission of waste. Air pollution, water pollution, deteriora-tion of the soil, and so forth, became topics that started worrying usimmensely. The ‘‘irreversibility’’ of most of our domestic and industrial ac-tivities seemed to ask a price for remediation that could become too high, ifnot for the present generations, then for later ones. This insight developed asense of responsibility that went beyond political, national, or other specificinterests and seemed to be shared by all aware world citizens. Earlier, andtriggered by activities of the Club of Rome, computer simulations showed thepossible limits to growth for a growing world populationwith limited sources.The 1987 Brundtland Report, ‘‘Our Common Future,’’ emphasized our res-ponsibility for future generations and pointed to the need for ‘‘sustainabledevelopment.’’ This showed the emergence of a trilemma—with economicgrowth, need for resources, and care for the environment in a delicate balance.The Sun as a renewable source of energy became more and more prominent,as exemplified in Japan’s massive New Sunshine Programme and by the

iii

emergence of ‘‘green chemistry,’’ a development to fulfill our needs forchemicals in a sustainable way.

Our desire to write this book originated in the aforementioned need toincrease the efficiency of industrial processes. Thermodynamics, in particularthe Second law, seemed indispensable to find one’s way in a labyrinth—or soit seemed—of resource and process alternatives. But with the emergence of theworldwide call for sustainability, our interest extended to include factorsother than efficiency to deal with this concept. In doing so, we discovered thatin nature energy and chemistry are more or less synonymous and that naturehas its own ways to be sustainable. However complex its ways and processes,nature is the example and the source of inspiration for developing from anindustrial society to what some like to call a metabolic society: a society thatmakes use of an immaterial energy source and recycles its products, includingits waste. This is not only a fascinating challenge but, more importantly, anecessity! Efficiency will be an important factor, as there are serious indica-tions that the world’s ecological opportunity to exploit the Sun as a resource islimited and may already have been spent.

ACKNOWLEDGMENTS

First we wish to express our appreciation to Emeritus Professor Kazuo Ko-jima from Nihon University in Tokyo for his great interest in the subject andhis steady efforts to convince us that we should trust our work and insights towrite this book.

We acknowledge AKZO Nobel for trusting us to teach its processengineers the principles of the thermodynamic efficiency of chemical processesandDSMas the first multinational company to let us apply these principles toits urea synthesis process. This triggered many research activities in ourgroup, and we benefited from the excellent textbook by Smith and Van Nessand the small monograph by J. D. Seader. Deeper insights into irreversiblethermodynamics was obtained from the monographs by Prigogine andKatchalsky. Our interest in sustainability was triggered by Unilever’s HansBroekhoff, who asked us the question that was half the answer. Yoda’s bookTrilemma, on sustainable development, was an eye-opener and moved us to ahigher level of abstraction in our thinking. Isao Shiihara, former generalmanager of the Osaka National Research Institute, introduced us to Japan’simpressive new energy research and development programs and institutes.Herman van Bekkum introduced us to green chemistry and Alexis DeVos tothe thermodynamics of solar radiation. The invaluable monographs bySchrodinger, Fast,Morowitz, and Lehninger introduced us to the concepts ofenergy flow in biology. Stephan Baumgartner and Robert Ayres contributed

Prefaceiv

to our insight into aspects of economics in sustainable development thanks tothe unsurpassed opportunities of the Gordon Research Conferences.

Our Ph.D. student Sona Raeissi gave us the inspiration for the design ofthe book’s cover.Management assistant Astrid Barrow assumed patiently butdeterminedly the responsibility for the electronic processing of our text. Fi-nally, we wish to mention the numerous students and postdoctoral fellowswho engaged themselves with great enthusiasm in the many studies that ul-timately became part of our education in this application from the wonderfulworld of thermodynamics.

Jakob de Swaan AronsHedzer van der Kooi

Krishnan Sankaranarayanan

Preface v

Contents

Preface iiiIntroduction ix

I. Basics

1. Introduction 12. Thermodynamics Revisited 73. Energy ‘‘Consumption’’ and Lost Work 234. Entropy Generation: Cause and Effect 335. Reduction of Lost Work 47

II. Thermodynamic Analysis of Processes

6. Exergy, a Convenient Concept 597. Chemical Exergy 738. Simple Applications 83

III. Case Studies

9. Energy Conversion 9710. Separations 12311. Chemical Conversion 14712. A Note on Life Cycle Analysis 167

IV. Process Sustainability

13. Sustainable Development 17514. Efficiency and Sustainability in the Chemical Process

Industry 20315. Solar Energy Conversion 215

vii

16. Biomass Production and Conversion 23117. Green Chemistry 24718. Economics, Ecology, and Thermodynamics 257

V. Future Trends

19. Future Trends 285

Index 297

Contentsviii

Introduction

Somewhere in the South Pacific a group of castaways reaches an uninhab-ited island after a storm destroyed their ship. They settle on this island butearly on disputes over the way of life splits them into two groups. One groupsettles in the North and the other group settles in the South. A small creeksplits the island in half and marks their spheres of existence. The group inthe North lives a lavish life, builds many wooden houses, and consumesthe bounty of the island. The group in the South lives a slightly less lavishlife, but returns to the land whatever it takes (resource ‘‘recycling’’). Whena tree is felled for lumber purposes, a set of trees is planted to replace theold one and ensure future lumber. When seeds are eaten, a fixed proportionis planted to ensure harvest the next year. The group in the North, on theother hand, consumes without replenishing and after ten years has turnedthe North side of the island into a desolate wasteland where the annualrainfall causes mudslides, and is also faced with a famine since no seeds orfruits are left. This group then decides to make peace with the Southernersand adopts their way of life.

Today, the way the Northerners consumed is very similar to our con-sumption habits. We consume but we do not always return to ensure a fu-ture supply (i.e., consumption of fossil fuels increases CO2 levels; felling oftrees without replanting removes CO2 sinks and disrupts the ecosystem). Butjust like the Northerners, at some point, the bounty will stop for a variety ofpossible reasons. Unfortunately, mankind does not have a friendly neighborwho can help us out. We must help ourselves by adopting a sustainable wayof life.

Angela Merkel, physicist and former German Minister of Environ-ment, defined sustainable development as using resources no faster than theycan regenerate themselves and releasing pollutants to no greater extent thannatural resources can assimilate them. Living systems prevail in a permanentstate of nonequilibrium with respect to their environment and sustain thisstate by a permanent energy source. Ultimately, the Sun is responsible for

ix

the energy of living systems (photosynthesis of plants, which stand at thebase of the food pyramid). Solar radiation sustains the biosphere of ourplanet. In a way, our planet is a metabolic society, a living entity thatabsorbs energy from the Sun and sustains life by material cycles involvingCO2, H2O, etc., which are consumed and emitted by various metabolicsociety members. Unfortunately, present-day human civilization is notsustainable, since material cycles are no longer closed, but very much openand have upset the balance in the metabolic society. Perhaps man can learnfrom nature and become part of the metabolic society.

Jakob de Swaan AronsHedzer van der Kooi

Krishnan Sankaranarayanan

Introductionx

1Introduction

Learn the fundamentals of the game and stick to them. Band-Aid reme-dies never last.

—Jack Nicklaus

Some time ago we were teaching an advanced thermodynamics course toprocess technologists of AKZO NOBEL. Subjects included phase equilib-ria, the thermodynamics of mixtures, and models from molecular thermody-namics applied to industrial situations. The question was raised whether sometime could be spent on the subject of ‘‘exergy analysis of processes,’’ then asubject with which we were less familiar because energy-related issues fellless within the scope of our activities. We fell back on a small monograph bySeader [1] and the excellent textbook by Smith and Van Ness [2], who dedi-cated the last chapter not so much to exergy but to the thermodynamic analy-sis of processes. Concepts such as ideal work, entropy production, and lostwork were clearly related to the efficient use of energy in industrial processes.The two industrial examples given—one on the liquefaction of natural gas,the other on the generation of electricity in a natural gas-fired power station—lent themselves very well for illustrative purposes but also for applying theexergy concept and exergy flow diagrams [3, 4]. The latter concepts quite ap-pealed to us because of their instrumental and visual power in illustrating thefate of energy in processes (Fig. 1).

After this experience in industry, we started to include the subject inadvanced courses to our own chemical engineering students in Delft. A col-league had pointed out to us that the design of a process is more valuable ifthe process has also been analyzed for its energy efficiency. For mechanicalengineers, who were traditionally more engaged in energy conversion pro-cesses, this was obvious; for chemical engineers, until then more concernedwith chemical conversion processes, this was relatively new. The subject grewin popularity with our students because it became more and more obviousthat the state of the environment and energy consumption are closely related

1

and that excessive energy consumption appeared to be one of the most im-portant factors in affecting the quality of our environment.

In performing such an analysis, either for industry, such as in DSM’surea process, or out of own curiosity, we became more and more aware ofthe very important role that the second law is playing in our daily lives andhow the thermodynamics of irreversible processes, until then for us a beau-tiful science but without significant applications, appeared to have a high‘‘engineering’’ content. Atkins’ statement that the second law is the drivingforce behind all change [5] had a lasting impact on us, as much as Good-stein’s suggestion [6] that the second law may well turn out to be the centralscientific truth of the 21st century. We discovered the importance of therelation between results from classical, engineering, and irreversible thermo-

Figure 1 Grassmann diagram for the Linde liquefaction process of methane. Onethousand exergy units of compression energy result in 53 exergy units of liquid

methane. The thermodynamic efficiency of this process is 5.3%. The arrowed curves,bent to the right, show the losses in the various process steps.

Chapter 12

dynamics as we have tried to make visible in what we like to call ‘‘the magictriangle’’ behind the second law (Fig. 2).

Later, when we were struck by the observation that complex industrialschemes and life processes or living systems have much in common, ourattention was again attracted to the meaning of the second law and the roleof entropy production. This led us to the topic of energy flow in biology andthe invaluable monographs by Schrodinger [7] and Morowitz [8]. At onepoint we could recognize in a common industrial operation, such as dis-tillation, for example, some aspects of living systems, at least with regard tothe role of energy.

This part of our education had come in a timely fashion, as becameapparent when more and more often the words ‘‘sustainability’’ and ‘‘sus-tainable development’’ were brought in relation with the efficient use ofenergy. We were forced to see our analysis in the light of these concepts andto make efforts to extend our analysis to indicate, in quantitative terms, theextent to which processes or products are not only efficient but also contributeto sustainable development. Again we were stimulated by ideas and questionsfrom colleagues within multinational industries, in particular Shell andUnilever. All these elements and influences can be found in this monographand its structure.

The first part of the book, Basics, reviews the main results of classicalthermodynamics and identifies the important concepts of ideal work, lostwork, and entropy generation, from using and combining the first and sec-ond laws for flowing systems. Having identified these concepts, we furtherinterpret them in everyday technical terms by using the main results of irre-versible thermodynamics. After reviewing possible ways to minimize the

Figure 2 The magical triangle behind the second law. The relation between resultsfrom classical, engineering, and irreversible thermodynamics (see Chapter 4).

Introduction 3

work lost, we conclude this part by giving attention to the thermodynamiccost of performing a process in finite time and space.

Part II, Thermodynamic Analysis of Processes, discusses the thermo-dynamic efficiency of a process and how efficiency can be established andinterpreted. Next, a very useful thermodynamic property, called exergy oravailable work, is identified that makes it relatively easy to perform such ananalysis. Finally, some simple examples are given to illustrate the conceptand its application in the thermodynamic or exergy analysis of processes.

Part III, Case Studies, takes these illustrations a bit further, namely bydemonstrating the analysis for some of the most important processes inindustry, energy conversion, separations, and chemical conversion.

Part IV, Process Sustainability, deals with the challenging and intrigu-ing concepts of sustainability and sustainable development. After drawing arather bleak picture of the state of the industry, including the chemicalindustry, with regard to sustainability, we show how thermodynamics cangive us a quantitative insight and provide us with parameters that show uswhat is meant by a sustainable industry. This analysis quickly leads us to theinsight of the need for immaterial, renewable resources for energy, with thesun as the most prominent source. The various ways to convert solar energyinto other forms of energy, or to exploit it in the conversion of matter, arediscussed and an analysis is given of the conversion possibilities of biomass.Next a discussion is given on the subject of ‘‘green chemistry,’’ with majorattention for answering the question of how ‘‘green’’ (sustainable) greenchemistry is. The book concludes with a discussion on the role that econom-ics can play on the road to progress as it now appears to be more concernedwith serving short-term interest rather than those of the long term [9].

REFERENCES

1. Seader, J.D. Thermodynamic Efficiency of Chemical Processes, Industrial Energy-Conservation Manual 1; Gyftopoulos, E.P., Ed.; MIT Press: Cambridge, MA,1982.

2. Smith, J.M.; VanNess, H.C.; Abbott, M.M. Introduction to Chemical EngineeringThermodynamics, 4th ed.; The McGraw-Hill Companies Inc.: New York, 1987.

3. Sussman, M.V. Availability (Exergy) Analysis, A Self Instruction Manual; Mul-

liken House: Lexington, MA, 1985.4. de Swaan Arons, J.; van der Kooi, H.J. Exergy Analysis. In Adding Insight and

Precision to Experience and Intuition, in Precision Process Technology. Per-spectives for Pollution Prevention; Weijnen, M.P.C., Drinkenburg, A.A.H., Eds.;

Kluwer Academic Publishers: Dordrecht, 1993; 83–113.5. Atkins, P.W. Educating Chemists for the Next Millenium. ChemTech, July

1992, 390–392.

Chapter 14

6. Goodstein, D. Chance and Necessity. Nature 14 April 1994, 368, 598.7. Schrodinger, E. What Is Life?; Cambridge University Press: Cambridge, U.K.,

1980.

8. Morowitz, H.J. Energy Flow in Biology. In Biological Organisation as a Problemin Thermal Physics; OxBow Press: Woodbridge, CT, 1979.

9. Faber, M.; Proops, J.L.R.; Baumgartner, S. Chapter 7: All Production Is Joint

Production, in Sustainability and Firms. In Advances in Ecological Economics;Faucheux, S., Gowdy, J., Nicolaı, I., Eds.; Edwar Elgar: Cheltenham, U.K.,1998.

Introduction 5

2Thermodynamics Revisited

In this chapter we briefly review the essentials of thermodynamics and itsprincipal applications. We cover the first and second laws and discuss themost important thermodynamic properties and their dependence on pres-sure, temperature, and composition, being the main process variables.Change in composition can be brought about with or without transforma-tion of phases or chemical species. The common structure of the solution ofa thermodynamic problem is discussed.

1 THE SYSTEM AND ITSENVIRONMENT

In thermodynamics we distinguish between the system and its environ-ment. The system is that part of the whole that takes our special interestand that we wish to study. This may be the contents of a reactor or a sepa-ration column or a certain amount of mass in a closed vessel. We definewhat is included in the system. The space outside the chosen system or, moreoften, a relevant selected part of it with defined properties, is defined as theenvironment.

Next we distinguish between closed, open, and isolated systems. All aredefined in relation to the flow of energy and mass between the system and itsenvironment. A closed system does not exchangematter with its environment,but the exchange of energy (e.g., heat or work) is allowed. Open systems mayexchange both energy and matter, but an isolated system exchanges neitherenergy nor mass with its environment.

7

2 STATES AND STATE PROPERTIES

The system of our choice will usually prevail in a certain macroscopic state,which is not under the influence of external forces. In equilibrium, the statecan be characterized by state properties such as pressure (P) and tempera-ture (T ), which are called ‘‘intensive properties.’’ Equally, the state can becharacterized by extensive properties such as volume (V ), internal energy (U ),enthalpy (H), entropy (S ), Gibbs energy (G ), and Helmholtz energy (A).These properties are called ‘‘extensive’’ because they relate to the amount ofmass considered; once related to a unit amount of mass, they also becomeintensive properties.

The equilibrium state does not change with time, but it may changewith location as in a flowing system where P, T, and other state propertiescan gradually change with position. Then we speak of a steady state. If thestate temporarily changes with time, as in the startup of a plant, we call it a‘‘transient’’ state.

If an isolated system is in a nonequilibrium state, its properties willusually differ from its equilibrium properties and it is not stable. If such asystem can absorb local fluctuations, it is in a metastable state; otherwise, thesystem and state are called unstable.

3 PROCESSES AND THEIR CONDITIONS

Often our system of interest is engaged in a process. If such a process takesplace at a constant temperature, we speak of an isothermal process. Equally,the process can be defined as isobaric, isochoric, isentropic, or isenthalpic ifpressure, volume, entropy, or enthalpy, respectively, remains unchangedduring the process. A process is called ‘‘adiabatic’’ if no heat exchange takesplace between the system and its environment. Finally, a process is called‘‘reversible’’ if the frictional forces, which have to be overcome, tend to zero.The unrealistic feature of this process is that energy and material flows cantake place in the limit of driving forces going to zero; for example, in anisothermal process, heat can be transferred without a temperature differencewithin the system or between the system and its environment. More realistic,in a process is that frictional forces have to be overcome, requiring finite‘‘driving forces’’ as DP, DT, DG, or when driving forces are already present inthe system, this leads to processes where spontaneously is given in to suchforces as in a spontaneous expansion, mixing process, or reaction. Such pro-cesses are called ‘‘irreversible’’ processes and are a fact of real process life.As we will see later, the theory of irreversible thermodynamics identifies the

Chapter 28

so-called thermodynamic forces, for example, D(1/T ) instead of DT, and theassociated flow rate—in this instance, the heat flow Q.

4 THE FIRST LAW

Thermodynamics is solidly founded on its main laws. The first law is the lawof conservation of energy. For a closed system that receives heat from theenvironment,Qin, and performs work on the environment,Wout, we can write

DU ¼ Qin �Wout ð1Þ

Heat and work are forms of energy in transfer between the system and theenvironment. If more heat is introduced into the system than the system per-forms work on the environment, the difference is stored as an addition to theinternal energyU of the system, a property of its state. In amore abstract way,the first law is said to define the fundamental thermodynamic state property,U, the internal energy.

Equation (1), in differential form, can be written as

dU ¼ yQin � yWout ð2Þ

The y-character is used to indicate small amounts of Q and W because heatand work are not state properties and depend on how the process takesplace between two different states.

If the process is reversible and the sole form of work that the system canexert on its environment is that of volume expansion, then dW rev

out ¼ PdV: If,in addition, the process is isobaric, PdV = d(PV ) and

dQrevin ¼ dðUþ PV Þ ¼ dH ð3Þ

The enthalpy H is defined as H u U + PV and is a property of state derivedfrom the fundamental propertyU. If heat is stored reversibly and isobaricallyin a system, it is stored as an increase in the system’s H-value. H has beendefined for our convenience; it has no fundamental meaning other than thatunder certain conditions its change is related to the heat absorbed by thesystem. It can be shown that the specific heat at constant volume and pressure,cv and cp, respectively, can be expressed as

cv ¼ AU

AT

� �V

and cp ¼ AH

AT

� �P

ð4Þ

Thermodynamics Revisited 9

For process engineering and design, it is important to know how enthalpyis a function of pressure, temperature, and composition. The last variable isdiscussed later. It can be found in any standard textbook that the differentialof H can be expressed as a function of the differential of T and P as follows:

dH ¼ cpdTþ V� TAV

AT

� �P

� �dP ð5Þ

The first term depends on what is sometimes called the caloric equationof state, describing how intramolecular properties, the properties within themolecules, are a function of the state variables. The expression in bracketsrequires the mechanical equation of state, which expresses the dependency ofa property, for example,V on the intermolecular interactions, the interactionsbetween molecules. Process simulation models usually contain informationand models for both types of equation of state.

Most often we are not interested in the ‘‘absolute’’ value of H, butrather in its change, DtrH. The subscript ‘‘tr’’ refers to the nature of thechange. If the change involves temperature and/or pressure for a one phasesystem only, no subscript is used for D. But in case of a phase transition, ofmixing, or of a chemical reaction, the subscript is used and may read ‘‘vap’’for vaporization, ‘‘mix’’ for mixing, or ‘‘r’’ for reaction, and so forth.

When a superscript is used as in DtrHo, this indicates that the change

in H is considered for a transition under standard pressure, which usually ischosen as 1 bar. In the case of chemical reactions, the supercript o refers tostandard pressure and to reactants and products in their pure state or other-wise defined standard states such as infinitely dilute solutions.

Finally, we present the first law for open systems as in the case ofstreams flowing through a fixed control volume at rest [1]

dU

dt

� �cv

¼Xin

m:i hi þ u2i

2þ gzi

� �

�Xout

m:j hj þ

u2j2þ gzj

!ð6Þ

þXQ:in �

XQ:out þ

XW:sh;in �

XW:sh;out

For one ingoing and outgoing stream in the steady state (Fig. 1), this equa-tion simplifies into

m:

DHþ Du2

2þ gDz

� �¼ Q

:in �W

:out ð7Þ

wherem:refers to the mass flow rate considered, u is the velocity of the flowing

system, and z is its height in the gravitational field,whereasD refers to out� in.

Chapter 210

5 THE SECOND LAW AND BOLTZMANN

The second law is associated with the direction of a process. It defines thefundamental property entropy, S, and states that in any real process thedirection of the process corresponds to the direction in which the total en-tropy increases, that is, the entropy change of both the system and environ-ment should in total result in a positive result or in equation form

DSþ DSenvironment ¼ Sgenerated ð8ÞSgenerated > 0 ð9Þ

In other words, every process generates entropy. The best interpretation, inour opinion, of this important law is given by adopting a postulate byBoltzmann:

S ¼ k lnV ð10ÞThis equation expresses the relation between entropy and the thermodynamicprobability V and where k is Boltzmann’s constant. If in an isolated vessel,filled with gas, at t = 0 half of the molecules are nitrogen, the other half areoxygen, and all nitrogen molecules fill the left half of the vessel whereas alloxygen molecules fill the right half of the vessel, then this makes for a highlyunlikely distribution, that is, one of a low thermodynamic probability V0.

Figure 1 Changes in steady-state flow.

Thermodynamics Revisited 11

As time passes, the system will evolve gradually into one with an even dis-tribution of all molecules over space. This new state has comparatively a highthermodynamic probability V, and the generated entropy is given by

Sgenerated ¼ S nal � Soriginal ¼ kln V=V0ð Þ ð11ÞStandard textbooks give ample examples of how V can be calculated [1].

Notice that the direction of the process and time have been defined:This has been called the arrow of time [2]. Time proceeds in the direction ofentropy generation, that is, toward a state of greater probability for the totalof the system and its environment, which, in the widest sense, makes up theuniverse. Finally, we wish to point out that an interesting implication of Eq.(10) is that for substances in the perfect crystalline state at T = 0 K, thethermodynamic probability V = 1 and thus S = 0.

6 THE SECOND LAW AND CLAUSIUS

As the first law is sometimes referred to as the law that defines the funda-mental thermodynamic property U, the internal energy of the system, thesecond law is considered to define the other fundamental property, the en-tropy S. Classical thermodynamics, via Clausius’s thorough analysis [3] ofthermodynamic cycles that extract work from available heat, has producedthe relation between S and the heat added reversibly to the system at a tem-perature T:

dS ¼ yQrevin

Tð12Þ

This relation plays an important role in the derivation of the universal andfundamental thermodynamic relation

dU ¼ TdS� PdV ð13Þwhich is often called the Gibbs relation. This relation is instrumental inconnecting the changes between the most important thermodynamic stateproperties.

From this relation the differential dS can be expressed as the followingfunction of the differentials of pressure and temperature:

dS ¼ CP

TdT� AV

AT

� �P

dP ð14Þ

P, T, and also composition are the state variables most often used to char-acterize the state of the system, as they can be easily measured and con-

fi

Chapter 212

trolled. As we show in Part II, Eqs. (5) and (14) are important to perform thethermodynamic analysis of a process. DTS

0298 expresses the change in entropy

of a reaction at 298K and at standard pressure. The reaction is defined to takeplace between compounds in their standard state, that is, in the most stableaggregation state under standard conditions, like liquid water for water at298 K and 1 bar. Analogous to Eq. (6) for the first law for open systems, thesecond law reads

dS

dt

� �cv

¼Xin

m:iSi �

Xout

m:jSj

þXin

ZdQ:k

T�X

out

ZdQ:l

Tþ S

:generated

ð15Þ

and simplifies to Eq. (8) for single flows in and out the control volume in thesteady state.

Finally, equilibrium processes can be defined as processes between andpassing states that all have the same thermodynamic probability. On the onehand, these processes proceed without driving forces; on the other hand, andthis is inconsistent and unrealistic, there is no incentive for the process toproceed. These imaginary processes function only to establish the minimumamount of work required, or the maximum amount of work available, inproceeding from one state to the other.

7 CHANGE IN COMPOSITION

So far our discussion of thermodynamic concepts has referred to systems thatdid not seem to change with composition, only with pressure P, temperatureT, or the state of aggregation. Thermodynamics, however, is much more gen-eral than being limited to these conditions, fortunately, for changes in com-position are the rule rather than the exception in engineering situations. Purehomogeneous phases maymix, and a homogenousmixture may split into twophases. A homogeneous or heterogeneous mixture may spontaneously reactto one or more products. In all these cases changes in composition will takeplace. This part of thermodynamics is usually referred to as ‘‘chemical’’ ther-modynamics, and its spiritual father is Josiah Willard Gibbs [4]. It has beenthemerit of Gilbert Newton Lewis [5] to ‘‘decipher’’Gibbs’ achievements andto translate these into readily applicable practical and comprehensible con-cepts such as the Gibbs energy of a substance i, or the individual thermody-namic potential Ai, fugacity fi, or activity ai, concepts now widely used inprocess design. The thermodynamic or chemical potential can be consideredto be the decisive property for an individual molecular species transport or

Thermodynamics Revisited 13

chemical behavior. It has been one of the main achievements of John Praus-nitz [6] to be instrumental in quantifying thermodynamic properties for readyapplication by taking into account the molecular characteristics and proper-ties of those molecules making up the mixture in a particular thermodynamicstate. This branch of thermodynamics is often referred to as ‘‘molecular ther-modynamics,’’ and many consider John Prausnitz as one of the most promi-nent amongst its founding fathers.

If a mixing process or chemical transformation is brought about, spon-taneously or by applying work on the system, the process will take place withentropy generation:

Sgenerated > 0 ð9Þand the total entropy will tend to a maximum value that will be reached forthe equilibrium state.

Indeed, for different molecules, which otherwise are nearly the same,such as isomers, or molecules of about the same size, polarity, or other prop-erties, the thermodynamic probability of the mixed state at the same P and Tis much larger than that of the respective pure states (in molar units):

DmixS ¼ Sgenerated ¼ RlnVmixed

V separatedð16Þ

with Vmixed >>> Vseparated.If the change is in composition only, at constant P and T, and confined

to the system we wish to consider, for instance, in a mixer, separation col-umn, or a reactor, then a system property G, the Gibbs energy, can be iden-tified and has been defined as follows:

G u U� TSþ PV ð17ÞIt has the property that in time (t) and at constant pressure and temperature ittends to a minimum value that will be reached when the system has reachedequilibrium (Fig. 2);

GP;T ! min ð18Þor

dGP;T

dtV 0 ð19Þ

If we consider a chemical reaction that takes place in a homogeneous mix-ture, the equilibrium composition of the mixture can be found from theequality condition in Eq. (19) if the dependency of G on the composition isknown.

Chapter 214

If the process of mixing takes place with negligible change of the inter-nal energyU and volumeV, we speak of ideal mixing and it can be shown thenthat for 1 mole of mixture

DmixSideal ¼ �RXxilnxi ð20Þ

in which xi is the molar fraction of constituent i in the mixture and R is theuniversal gas constant. For an ideal mixture, Dmix U

ideal and Dmix Videal are

zero for mixing at constant P and T, and so Dmix Gideal is given by

DmixGideal ¼ RT

Xxilnxi ð21Þ

Notice thatDmixHideal is also zero and thus, with Eq. (3) in mind, ideal mixing

at constant P and T will take place without heat effects.For deviations from ideal mixing, the excess property ME is defined as

ME ¼ DmixM� DmixMideal ð22Þ

An important excess property is the excess Gibbs energy GE. Many modelshave been developed to describe and predict GE from the properties of themolecules in the mixture and their mutual interactions. GE models oftenrefer to the condensed state, the solid and liquid phases. In case significantchanges in the volume take place upon mixing, or separation, the Helmholtzenergy A, defined as

A u U� TS ð23Þand its excess property AE are the preferred choices for describing the pro-cess. This requires an equation of state that expresses the volumetric be-

Figure 2 The Gibbs energy G on approaching equilibrium.

Thermodynamics Revisited 15

havior of the mixture as a function of pressure, temperature, and composi-tion. For the models most applied in practice for GE and AE, the reader isreferred to Ref. [7].

Partial molar properties take a special place in the thermodynamics ofmixtures and phase equilibria. They are defined as

Mi uAðnMÞAni

� �P;T;nj p i

ð24Þ

The best-known example is the partial molar Gibbs energy, better knownas the earlier-mentioned thermodynamic potential A. The thermodynamicpotential of component i in a homogeneous mixture is

Ai u Gi ¼ AðnGÞAni

� �P;T;nj p i

ð25Þ

An important condition for phase equilibria is

AiV ¼ AiVV ¼ AiVVV ¼ . . . ð26Þor in terms of the fugacity in mixtures

f iV ¼ f i

VV ¼ . . . ð27Þin which equations the primes indicate the respective phases. Fugacity andactivity (see below) are directly related to the thermodynamic potential. Thelatter property has the dimension of Joules per mole, whereas fi has thedimension of pressure and ai is dimensionless.

The last equation, applied to a vapor–liquid equilibrium, reads

fiyiP ¼ cixiPsati fsat

i expV S

i P� Psati

� �AT

� �ð28Þ

which simplifies to Raoult’s law for ideal gas behavior, for which the fugacitycoefficients fi and fi

sat are equal to 1, and ideal mixing in the liquid state, forwhich the activity coefficient gi equals 1, and the Poynting factor (theexponential in Eq.28), with Vi

S the liquid-phase molar volume is approxi-mately unity:

yiP ¼ xiPsati ð29Þ

The fugacity coefficient fi can be calculated from a valid equation of state;the activity coefficient gi can be derived from an applicable GE expression.The activity ai is the product of gi and xi.

The property known as the Gibbs energy G, and defined by Eq. (17),plays an important role in describing on the one hand the transformationbetween phases where species stay the same but distribute differently over the

Chapter 216

phases present, such as vapor and liquid, on the other hand in transforma-tions where species change identity, the chemical reaction. Chemical reactionsand phase transformations both proceed in the directions that fulfill Eqs. (18)and (19).

For a chemical reaction

rAAþ mBBþ . . .! mjJþ mkKþ . . . ð30Þin which ri is the stoichiometric coefficient of species i, defined as positive fora product and negative for a reactant, it can be shown that progress of thereaction can be characterized by a reaction property, the so-called degree ofadvancement of reaction, which is defined as [1]

dn ¼ dnimi

ð31Þ

s and the chemical reaction velocity vchem are related by

vchem ¼ dndt

ð32Þ

Equilibrium is reached for (Fig. 3)

dG

dn¼ 0 ð33Þ

and

vchem ¼ 0 ð34ÞIf G is known as function of composition, the position of the chemical equi-librium can be determined with the help of Eq. (33), which is instrumental in

Figure 3 The Gibbs energy G and the degree of advancement of reaction s.

Thermodynamics Revisited 17

finding the equilibrium composition. It can be shown that chemical equilib-rium is characterized by the equationX

miAi ¼ 0 ð35ÞFrom this the chemical equilibrium constant at temperature T

KT ¼ Yfi=f

0i

� �mi ð36Þ

can be identified as

RT lnKT ¼ �DrG0T ð37Þ

The dependency on T is given by

d lnKT

d 1T

¼ � DrH0T

Rð38Þ

Knowledge of these changes in standard Gibbs energy and enthalpy al-lows one to calculate the equilibrium composition and its variation withtemperature.

8 THE STRUCTURE OF A THERMODYNAMICAPPLICATION

We now briefly discuss how thermodynamics can work for us or, better, howthermodynamics functions to solve a problem where thermodynamics canhelp to provide the answer. We wish to illustrate this for a relatively simpleproblem: how much work is required to compress a gas (Fig. 4) from a low toa high pressure. Figure 5 schematically gives the path to the answer and thestructure of the solution. In fact, the same steps will have to be taken to applythermodynamics to problems such as the calculation of the heat releasedfrom or required for a process, of the position of the chemical or phase equi-librium, or of the thermodynamic efficiency of a process.

In our case the task is to calculate the amount of work required tocompress a gas at pressureP1 and temperature T1 to a pressureP2.We turn tothe first law in the version of Eq. (7), which allows us to translate the original,technical, question into one of thermodynamics:

Win ¼ DHþQout ð39ÞWe assume that the compression is adiabatic: that is, will take place withoutexchange of heat with the environment,Qout = 0. So the first law tells us thatWin is known if we know the change in enthalpy of the gas. For this we need toknow how the gas enthalpy is a function of pressure and temperature.

Chapter 218

Figure 4 The compressor.

Figure 5 The structure of a thermodynamic application.

Thermodynamics Revisited 19

Assuming, for simplicity, that the gas behaves like an ideal gas, for which theenthalpy is not a function of pressure, we end up with the relation

DH ¼ cp T2 � T1ð Þ ð40Þby which we have also assumed that the specific heat at constant pressure, cp,is not a function of temperature. Unfortunately, we do not know T2, and forthat we turn to the second law. As the process takes place adiabatically, wewrite Eq. (8) in the version

DSz 0 ð41ÞFirst we assume that the process takes place reversibly, and thus

DrevS ¼ 0 ð42ÞWith the assumptions that the gas behaves as an ideal gas and cp is not afunction of temperature, we may write

DrevS ¼ cplnT rev2

T1� Rln

P2

P1ð43Þ

These equations allow us to calculate T rev2 , DrevH, and thus W rev

in , the workrequired if the compression had taken place reversibly. But in the real processDS > 0, and according to Eq. (43), T2 must be larger than T rev

2 and DH >DrevH. Thus, Win > W rev

in . Usually, this is expressed in the compressor’sefficiency

g uW rev

in

Win< 1 ð44Þ

When this efficiency is known, and for a specific compressor it usually is,Win

can be calculated and with this T2. If we now turn again to Fig. 5, the fun-damental laws (step 1) were instrumental in translating the task, whereas thefundamental relations (step 2) that express how H and S are functions of Pand T provide us with equations to proceed to the answer. Usually, the gasdoes not behave as an ideal gas andwe needmodels (step 3) for what we earliercalled the mechanical equation of state and the caloric equation of state. Thiswill lead us to what we call handlable, as opposed to abstract, equations. Theabstract equations do not allow us to calculate anything, but the ‘‘handlable’’equations allow us to perform calculations if we know some numbers. Givencertain basic data, from experiment or predicted, and associated parameters,such as for expressing cp as a function of temperature (step 5), these equationsallow us to perform the computation (step 6) to complete the task and comeup with the answer to the original question. Steps 1 and 2 are extensively dis-cussed in textbooks of chemical engineering thermodynamics [1], step 3 falls

Chapter 220

within the subdiscipline of molecular thermodynamics [6] and step 5 fallswithin that of the prediction of thermodynamic properties as function ofcomposition and based on the molecular structure of the mixture’s constitu-ents and their mutual interactions [7].

We conclude this example with the observation that the second law forreal processes expresses that entropy generation is positive and that the impli-cation is that the real amount of work required is larger than that calculatedfor the reversible or ideal(ized) process. This suggests a relation between en-tropy generation and excess work. This relation is of fundamental significancefor the subject of this monograph, as we illustrate later.

REFERENCES

1. Smith, J.M.; van Ness, H.C.; Abbott, M.M. Introduction to Chemical Engi-

neering Thermodynamics, 4th Ed.; McGraw-Hill: New York, 1987.2. Blum, H.F. Time’s Arrow and Evolution; Harper: New York, 1962.3. Carnot, S. Reflections on the Motive Power of Fire and Other Papers on the

Second Law of Thermodynamics by R. Clausius and E. Clayperon; DoverPublications: New York, 1960.

4. Gibbs, J. Willard. Thermodynamische Studien; Wilhelm Engelmann Verlag:Leipzig, 1982.

5. Lewis, G.N.; Randall, M. Thermodynamics, as revised by Kenneth S. Pitzer andLeo Brewer; McGraw-Hill: New York, 1961.

6. Prausnitz, J.M.; Gomes de Azevedo, E.; Lichtenthaler, R.N. Molecular

Thermodynamics of Fluid Phase Equilibria, 3rd Ed.; Prentice Hall: EnglewoodCliffs, NJ, 1999.

7. Reid, R.C.; Prausnitz, J.M.; Poling, B.E. The Properties of Gases and Liquids,

4th Ed.; McGraw-Hill: New York, 1987.

Thermodynamics Revisited 21

3Energy ‘‘Consumption’’and Lost Work

1 INTRODUCTION

We all know what is meant by energy consumption. Most of us have to payenergy bills and we accept that we are charged for consuming energy just aswe are charged for consuming other things. But are we consuming energy?According to the first law of thermodynamics, energy cannot be created norannihilated. Then what is it that we consumed if it is not energy?

In a way the situation can be compared with consuming food. If wemade a thorough analysis of food consumption, we would conclude that itis not its mass that we have consumed, as the mass balance is not affected.Nor is it the energy that we have consumed as a properly performed energybalance will show. This led Erwin Schrodinger [1] to his somewhat desper-ate question: ‘‘If it is mass nor energy that we extract from food then whatis it . . .?’’

As should become clear from the following sections, it is not energythat we consume but its quality, by which is meant the extent to whichenergy is available for performing work. In the spontaneous combustion ofnatural gas, mass and energy are conserved, but the work stored andavailable in the chemical bonds of the gas will, to a large extent, get lost.By energy ‘‘consumption’’ we mean consumption of or decrease in availablework. Loss of available work is called lost work, Wlost. As we shall show,lost work can, in thermodynamic terms, be identified as the product of theentropy generated and the absolute temperature of the environment T0. Thisis expressed in the remarkable relation known as the Gouy–Stodola relation[2,3].

23

2 THE CARNOT FACTOR

Carnot allowed us to answer the following question: Which part of heat Q,available at a temperature T > T0, can at most be converted into usefulwork? Provided the process is cyclic and conducted reversibly, the maximumamount of work available is given by

W maxout ¼ Q 1� T0

T

� �ð1Þ

The factor 1 � (T0/T ) is often called the thermodynamic efficiency, butwe prefer to call it the Carnot factor.* For example, if heat is supplied at 600Kand the temperature of the environment is 300 K, the Carnot factor is 1/2. Wecould also say that in this instance the quality q of every Joule of heat is 1/2 J/J,if we wish to express that atmost half of the Joule of heat supplied can bemadeavailable for useful work with respect to our environment at T0:

q ¼ W maxout

Q¼ 1� T0

Tð2Þ

So we define the quality of heat supplied at a temperature level T>T0 asthe maximum fraction available for useful work. Baehr [4] has called this partof heat the exergy of heat. The remaining part is unavailable for useful workand is called anergy. It is the minimal part of the original heat that will betransferred as heatQmin

0 to the environment. In Baehr’s terminology, we couldsay that in this instance the ideal heat engine would achieve the followingseparation between useful and useless Joules:

Q ¼ Q 1� T0

T

� �þQ � T0

T

¼W maxout þQmin

0 ð3Þ¼ exergyþ anergy

Overall the cycle takes up an amount of energy Q, produces an amountof work Wmax

out , and releases an amount of heat Q�Wmaxout ¼ Qmin

0 at thetemperature T0 to the environment.

* The minimum amount of work, Wminin , required to transfer to the environment the amount of

‘‘heat’’ leaked in from the environment at T0 into a reservoir maintained at a temperature

T<T0 is

Wminin ¼ Q

T0

T� 1

� �

Chapter 324

This equation very nicely expresses the quality aspects of heat andmust have tempted Sussmann [5] to a statement much inspired by GeorgeOrwell in his famous novel Animal Farm [6]: ‘‘All Joules are equal but someJoules are more equal than others.’’ But, in a more earnest sense, thisobservation can also be found in discussions on energy policy [7]: ‘‘Thequality of energy (i.e. exergy)—and not only the quantity—as an objectiveand clear starting point, must be included in making policy choices.’’

Later it will become clear why this observation is important and howfar-reaching the implication is of making use of the distinction between bothquantity and quality of the various Joules involved in a process.

Equation (3) is an expression of the first law of thermodynamics forthe separation in useful and useless energy of the energy from heat.Equation (1) is clearly not an expression of the first law, but, as we shallsee later, an implication of the second law. In this context it is worthrecalling Baehr’s formulation of the first and second laws [4]:

1. The sum of exergy and anergy is always constant.2. Anergy can never be converted into exergy.

This unusual and much less-known formulation of the main laws ofthermodynamics serves the purpose of this book very well.

3 LESSONS FROM A HEAT EXCHANGER

Some important lessons from engineering thermodynamics can be learnedfrom the thermodynamic analysis of a heat exchanger. For illustrativepurposes we assume that the heat is exchanged between a condensing fluidat a temperature Thigh and an evaporating fluid at a temperature Tlow, withThigh > Tlow > T0 (Fig. 1). The mass flow rates have been chosen such thatwithin the exchanger all high-temperature fluid condenses and all low-tem-perature fluid evaporates. The heat exchanger is not supposed to exchangeheat with the environment and thus operates adiabatically. For steady-stateoperation, if changes in kinetic and potential energy are small compared to theenthalpy changes, the energy balance can be written as

�mhighDHhigh þ �mlowDHlow ¼ 0 ð4Þ

The amount of heat exchanged and taken up by the evaporating fluid per unitof time, the heat flow rate

�Q, is positive and is given by

�Q ¼ �mlowDHlow

¼ � �mhighDHhigh

ð5Þ

Energy ‘‘Consumption’’ and Lost Work 25

and this amount flows spontaneously from Thigh to Tlow. At the hightemperature its exergy, or available work as Americans prefer to call it, is

Whigh ¼ Q 1� T0

Thigh

� �ð6Þ

At the low temperature its quality has decreased and the available work isnow less:

Wlow ¼ Q 1� T0

Tlow

� �ð7Þ

Thus, the exchange of heat has taken place with a rate of loss of availablework:

�Wlost ¼ �Whigh � �Wlow

¼ �Q 1� T0

Thigh

� �� 1� T0

Tlow

� �� �ð8Þ

¼ �Q � T01

Tlow� 1

Thigh

� �or per unit mass instead of per unit time:

Wlost ¼ Q � T01

Tlow� 1

Thigh

� �ð8aÞ

Figure 1 A heat exchanger in which the heat of condensation of a fluid at Thigh isexchanged with the evaporating fluid at Tlow. We assume that Thigh > Tlow > T0.

Chapter 326

From Fig. 2, in which the Carnot factor has been plotted against the amountof heat transferred, we can conclude that the work lost is represented by theenclosed area between the temperature levels Thigh and Tlow and the points ofentry and exit.

The factor between brackets in Eq. (8) can be identified as the ‘‘drivingforce’’ for heat transfer, but instead of the familiar DT = Thigh � Tlow, ourequation suggests that the thermodynamic driving force is D(1/T ) = (1/Tlow) � (1/Thigh), and thus Eq. (8a) shows that the amount of work lost isthe product of T0 and the product of Q and D(1/T ), namely the product ofthe flow and its driving force. This last product is one of the many that canbe identified with the help of irreversible thermodynamics, as we show inChapter 4. Another interesting observation is the following. If a body orflow isothermally absorbs a positive amount of heat, Qin at a temperature T,then its change in entropy is given by

DS ¼ Qin

Tð9Þ

With this equation in mind, we can read the last part of Eq. (8a) as

Wlost ¼ T0ðDSlow þ DShighÞ ¼ T0DS ð10Þin which DS is the entropy change of the heat exchanger. As the heatexchanger operates adiabatically, there is no associated change in entropy

Figure 2 The enclosed area represents the amount of lost work in this plot of the

Carnot factor against the heat transferred.

Energy ‘‘Consumption’’ and Lost Work 27

of the environment, DS0 = 0, and thus the second law according toEq. (2.8) reads

Sgenerated ¼ DS ð11ÞThis allows us to write for Eq. (10)

Wlost ¼ T0Sgenerated ð12ÞThis remarkable simple relation between the work lost and the entropyproduced in a process dates back to the beginning of the twentieth century,when it was independently derived by Gouy [2] and Stodala [3].

This equation is not restricted to the process of heat exchange butinstead has a universal validity. This is shown in the next section. The extentto which heat exchangers can contribute to the work lost in a process isclearly illustrated in Fig. 3. Here we observe that for the process of makingice, nearly 45% of the compressor work is lost in the evaporator andcondenser of the ammonia refrigeration cycle. Not many process technol-ogists associate lost work with heat exchange, but this example strikinglyshows that they should.

Figure 3 A refrigeration cycle to make ice from water with ammonia as theworking fluid or energy carrier. Nearly 45% of the compression power is lost due toheat exchange, in the evaporator and the condensor, respectively.

Chapter 328

As mentioned before, this thermodynamic analysis suggests thatD(1/T ), not DT, is the driving force behind heat flow, contrary to everydayengineering practice. We may then write that to a first approximation

Q ¼ kH � D 1

T� A ð13Þ

in which kH is the overall thermodynamic heat transfer coefficient and A isthe surface of exchange. If we introduce this expression in Eq. (8), we canwrite

Wlost ¼ kH � A � T0 D1

T

� �2

ð14Þ

This equation tells us that the amount of work lost in a heat exchanger is inthe first instance proportional to the square of the driving force, and so ifone wishes to be more economical with energy, the driving force should bemade smaller. On the other hand, Eq. (13) shows us that if we have to fulfilla certain heat transfer duty Q, the reduction of D(1/T ) must be compensatedeither by an exchanger material with better heat conduction properties (alarger kH) or with a larger surface for transfer. It is interesting how thesesimple equations express the economic need of optimizing between capitalcost and the cost of energy. The powerful role of thermodynamics herebecomes somewhat tempered by the role of economics. Both disciplines playa decisive role in the ultimate design of the heat exchanger.

4 LOST WORK AND ENTROPY GENERATION

We consider a steady flowingmedium onwhich an amount of work is exerted,Win (Fig. 4). Heat is only exchanged with the environment at a temperatureT0. We assume that the flow is not undergoing significant changes in velocitynor in height and therefore neglect the macroscopic changes in kinetic andpotential energy. The first law reads according to Eq. (39) of Chapter 2

Win ¼ DHþQ0 ð15ÞThe second law reads

Sgenerated ¼ DSþ DS0 ð16ÞWe combine the equations, making use of the relation

DS0 ¼ Q0

T0ð17Þ

Energy ‘‘Consumption’’ and Lost Work 29

and after eliminating Q0 and DS0, we arrive at the following equation:

Win ¼ DH� T0DSþ T0Sgenerated ð18ÞDH andDS express the changes in the flow’s enthalpy and entropy from state 1to state 2, for example,

DH ¼ HðP2T2Þ �HðP1T1Þ ð19ÞThe minimum amount of work to accomplish this change in conditions isapparently given by

Wminin ¼ DH� T0DS ð20Þ

The second law states that Sgenerated > 0; hence the real amount of workrequired must be larger:

Win ¼Wminin þ T0Sgenerated ð21Þ

The amount of work lost in the process is defined as

WlostuWin �Wminin ð22Þ

and thus we arrive at the relation

Wlost ¼ T0Sgenerated ð23ÞThis relation holds, of course, for the general exchange of work and heatbetween a flowing medium and its environment. The abstract formulation ofthe second law as in

Sgenerated > 0 ð24Þ

Figure 4 Work and heat are exchanged with the environment while a fluid isbrought from condition 1 at P1, T1 to condition 2 at P2, T2.

Chapter 330

has found here a clear and nonambiguous translation into terms widelyunderstood in the everyday world. After all, lost work in any process makes usrely more on energy resources such as coal, oil, natural gas, nuclear fuel, andso on. Knowing the prices of fuel, we can thus even translate entropygeneration into terms of monetary units, but then the concept becomes asshaky as the value of a currency, and so we shall refrain from doing this. Butthe observation has to be made.

At this point the need arises to become more explicit about the natureof entropy generation. In the case of the heat exchanger, entropy generationappears to be equal to the product of the heat flow and a factor that canbe identified as the thermodynamic driving force, D(1/T ). In the nextchapter we turn to a branch of thermodynamics, better known as irrevers-ible thermodynamics or the thermodynamics of the nonequilibrium state, toconvey a much more universal message on entropy generation, flows, anddriving forces.

5 CONCLUSION

The quality of heat is defined as its maximum potential to perform workwith respect to a defined environment. Usually this is the environmentwithin which the process takes place. The Carnot factor quantitativelyexpresses which fraction of heat is at most available for work. Heat in freefall from a higher to a lower temperature incurs a loss in this quality. Thequality has vanished at T0, the temperature of the prevailing environment.Lost work can be identified with entropy generation in a simple relation.This relation appears to have a universal value.

REFERENCES

1. Schrodinger, E.M. What Is Life?, Cambridge University Press: Cambridge,U.K., 1944.

2. Gouy, G. J. Phys. 1889, 8, 501.3. Stodola, A. Steam and Gas Turbines; McGraw-Hill: New York, 1910.4. Baehr, H.D. Thermodynamik; Springer-Verlag: Berlin,1988.

5. Sussmann, M.V. Availability (Exergy) Analysis, 3rd Ed.; Mulliken House: Lex-ington, MA, 1985.

6. Orwell, George, Animal Farm, Penguin Longman Publishing Company: Lon-

don, 1945.7. 1991 Annual Report of the Dutch Electricity Producers (SEP).

Energy ‘‘Consumption’’ and Lost Work 31

4Entropy Generation: Causeand Effect

In this chapter we first introduce the principles of irreversible or nonequilib-rium thermodynamics as opposed to those of equilibrium thermodynamics.Then we identify important thermodynamic forces X (the cause) and theirassociated flow rates J (the effect). We show how these factors are respon-sible for the entropy production rate and the work lost in processes. Thisgives an excellent insight into the origin of the incurred losses. We give at-tention to the relation between flows and forces and the possibility of cou-pling of processes and its implications.

1 EQUILIBRIUM THERMODYNAMICS

Equilibrium thermodynamics is the most important, most tangible result ofclassical thermodynamics. It is a monumental collection of relations betweenstate properties such as temperature, pressure, composition, volume, internalenergy, and so forth. It has impressed, maybe more so overwhelmed, many tothe extent that most were left confused and hesitant, if not to say paralyzed, toapply its main results. The most characteristic thing that can be said aboutequilibrium thermodynamics is that it deals with transitions between well-defined states, equilibrium states, while there is a strict absence ofmacroscopicflows of energy and mass and of driving forces, potential differences, such asdifference in pressure, temperature, or chemical potential. It allows, however,for nonequilibrium situations that are inherently unstable, out of equilibrium,but are kinetically inhibited to change. The driving force is there, but the flowis effectively zero.

33

Some confusionmay rise from the discussion of so-called reversible pro-cesses. Reversible processes take place in the limit of all driving forces going tozero. Most of us tacitly accept the terminology of ‘‘heat is isothermally trans-ferred’’ only to become aware in daily engineering practice that there is nosuch thing as isothermal heat transfer. In daily engineering practice heattransfer needs a temperature gradient, mass transfer needs a gradient in thethermodynamic potential, and chemical conversion needs a nonzero affinitybetween producs and reactants. In fact, all heat exchangers, separation col-umns, chemical reactors, and so forth work by the grace of driving forces,which can be defined by thermodynamics, as we shall see. It is the virtue ofirreversible thermodynamics to reconcile the results of equilibrium thermo-dynamics with the need to determine rates of processes encountered in processtechnology.

2 ON FORCES AND FLOWS: CAUSE AND EFFECT

In Section 3.3 we show that the entropy generation rate in the case of heattransfer in a heat exchanger is simply the product of the thermodynamicdriving force X=D(1/T ), the natural cause, and the resultant flow J=Q

�, a

velocity or rate. Selected monographs on irreversible thermodynamics, seee.g. [6], show how entropy generation also has roots in other driving forcessuch as chemical potential differences or affinities.

Katchalsky [1], for example, considers a system separated from the en-vironment by a rigid adiabatic wall. The system consists of two compart-ments 1 and 2, separated by a diathermal, elastic barrier that is permeable toone of the components in the system (Fig. 1). It can be shown that theentropy generation rate is given by

dSgen

dt¼ dQ1

dt

1

T1� 1

T2

� �þ dV1

dt

P1

T1� P2

T2

� �� dn1

dt

A1T1� A2

T2

� �ð1Þ

S�gen ¼ Q

�1 � D 1

T

� �þ V�1 � D P

T

� �þ n� � D � A

T

� �¼ S

iJiXi

ð2Þ

Here we have adopted the convention that Ji is the flow rate, a veloc-ity, of heat, volume, and matter and Xi is the corresponding affinity ordriving force D(1/T ), D(P/T ) and D(�A/T ). Irreversible thermodynamicssmoothly transforms into equilibrium thermodynamics in the limiting casewhen the driving forces are going to zero. Without driving forces, there willbe no macroscopic process and true equilibrium is established. The existenceof driving forces does not automatically imply flows. Inhibition by either

Chapter 434

physical or chemical barriers may prevent the occurrence of flow, even if thedriving force is not zero. These then are situations of instability. We speak ofa metastable system if it is locally stable but globally unstable and of anunstable system in the case of local instability (Fig. 2) [2].

We have not dealt yet with another driving force better known aschemical affinity. We recollect that the condition for chemical equilibrium ata certain pressure P and temperature T is given by [3]

SriAi ¼ 0 ð3Þ

In this equation vi and Ai stand, respectively, for the stoichiometric coeffi-cient and the thermodynamic potential of the ith component taking part inthe reaction. The convention is that vi is positive for a product and negativefor a reactant. The reaction will proceed to the right if AviAi is negative andto the left if this sum is positive. It is therefore convenient to define thechemical affinity A as

A ¼ �SriAi ð4Þ

When A is positive, the reaction should proceed to the right. When A = 0,chemical equilibrium prevails. Formulated in this way, A suits our percep-tion of chemical affinity perfectly. Another characteristic property is thedegree of advancement of reaction s [3]. The chemical reaction velocity andthe degree of advancement are related by

vch ¼ dndt¼ 1

vi

dnidt

ð5Þ

Figure 1 An isolated system separated in two compartments by a membrane.

Entropy Generation: Cause and Effect 35

It can be shown that the contribution to the entropy generation rate S�gen due

to the progress of a chemical reaction is given by

S�gen ¼ A

T� vch ð6Þ

vch will be positive if A is positive; with vch approaching zero, A will ap-proach 0; and with vch = 0, true chemical equilibrium has been establishedand A = 0. We have now identified a new driving force, A/T, which is anaddition to the driving forces we have already encountered, D(1/T ), D(P/T ),and D(�A/T ). The case of chemical affinity has stimulated some to call alldriving forces affinities, but we will not adopt this convention, because wethink that the word ‘‘affinity’’ should exclusively relate to chemistry.

When more reactions take place at the same time, the chemicalcontribution to S

�gen is given by

S�gen ¼ A1

T1� v1 þ A2

T2� v2 þ . . . ð7Þ

Each contribution to the total rate must be positive unless reactions are cou-pled. In the case of coupled reactions, one contribution may be negative (this

Figure 2 Example of a stable (a), metastable (b), and unstable (c) system.

Chapter 436

reaction goes uphill) as long as the other coupled reaction is downhill andhas a positive contribution large enough to make the sum positive. Later weshall see that this case is one of the great challenges for the chemical industryto cut down on energy consumption. Living systems make extensive use ofthis ingenious principle [7] and thus serve as a splendid example to meet thischallenge.

3 CAUSE AND EFFECT: THE RELATION BETWEENFORCES AND FLOWS

Although irreversible thermodynamics neatly defines the driving forcesbehind associated flows, it does not tell us about the relationship betweenthese two properties, which would complete the picture. Such relations havebeen obtained from experiment, and famous empirical laws have beenestablished like those of Fourier for heat conduction, Fick for simple binarymaterial diffusion, and Ohm for electrical conductance. These laws arelinear relations between force and associated flow rates that, close toequilibrium, seem to be valid. The heat conductivity, diffusion coefficient,and electrical conductivity, or reciprocal resistance, are well-known propor-tionality constants and as they have been obtained from experiment, theyare called phenomenological coefficients Lii,

Ji ¼ LiiXi ð8ÞNewton’s law is a special case, as Katchalsky points out [1]. Newton’s lawrelates force to acceleration:

f ¼ ma ð9ÞThis relation is restricted, however, to frictionless media. If frictional forcesare included, and acceleration is assumed to be damped out, an equally linearrelationship between velocity v and force f can be established as in Stokes’ law,which clearly falls in the above category.

Equation (8) may be rewritten as

Xi ¼ RiiJi ð10ÞIn this equation, just as in Newton’s law adapted for friction, the reciprocalof the phenomenological coefficient Lii has been introduced and acts as afriction coefficient, a resistance. Recalling the relations

W�lost ¼ T0S

�gen ð11Þ

and

S�gen ¼ S

iJiXi ð12Þ

Entropy Generation: Cause and Effect 37

a direct relation emerges between the work lost in the process and the fric-tions incurred:

W�lost ¼ T0 S

iRiiJ

2i ð13Þ

This equation expresses the fact that in a process with the various flowsJi, work is continuously dissipated to overcome the barriers, the resistance, orthe friction that all the processing such as heat andmass transfer and chemicalconversion introduce. In Chapter 5 we refer to this as the result of the ‘‘magictriangle.’’ There is no clearer way to illustrate the origin of the process’senergy bill, nor a better way to calculate it. This relation also defines the chal-lenge that in order to keep the energy bill as low as possible one should find, asBejan calls it, ‘‘the path of least resistance’’ [4].

4 COUPLING

So far we have discussed the relation between one driving force and what iscalled its conjugated flow. Experiments have empirically established manylinear relations between flows and conjugated forces. But experiments alsopointed to a possible extension of this linearity. Flow rate J1 might as well belinearly related to driving force X2 and flow rate J2 to X1, and so on. Suchobservations, according to Katchalsky [1], have been made, for example, forthe ‘‘interference’’ of electrical and osmotic behavior, of mass and heat flowand of electricity and heat flow. This led Onsager [5], chemical engineer andNobel laureate, to the formulation of the so-called phenomenologicalequations:

J1 ¼ L11X1 þ L12X2 þ . . . ð14ÞJ2 ¼ L21X1 þ L22X2 þ . . .

or

Ji ¼ Sn

k¼1LikXk ði ¼ 1; 2; . . . ; nÞ ð15Þ

An alternative formulation may be given according to

Xi ¼ Sn

k¼1RikJk ði ¼ 1; 2; . . . ; nÞ ð16Þ

in which the coefficients Rik represent generalized resistances or frictions. Lii

or Rii are coefficients between the conjugated flow and force. Lik and Rik areso-called coupling or interference coefficients. Onsager [5] shows that if this

Chapter 438

type of coupling takes place, a simple relation between the couplingcoefficients exists:

Lik ¼ Lki ð17Þor

Rik ¼ Rki ð18ÞA rule of thumb for the validity of linear relationships is that processesshould be slow and the thermodynamic states near equilibrium. But eventhen not all flows can be coupled. Coupling is limited to certain cases.Casimir shows that coupling is only possible between driving forces of thesame tensorial character, such as scalar, vectorial, and so forth. For moredetails, see [1].

An interesting question that immediately comes up is how couplingaffects Sgenerated and Wlost. Therefore, we recall that

S�gen ¼ S

n

i¼1JiXi ð19Þ

which is an unconditional relation. Next we assume a simple case of twopairs of conjugated flows and forces that are linearly related and coupled;thus

J1 ¼ L11X1 þ L12X2

J2 ¼ L21X1 þ L22X2

ð20Þ

S�gen ¼ J1X1 þ J2X2

¼ L11X21 þ ðL12 þ L21ÞX1X2 þ L22X

22 > 0

ð21Þ

The second law requirement that S�gen > 0 leads to the condition that

L11 > 0; L22 > 0 ð22Þand

ðL12Þ2 < L11L22 ð23ÞThis relation does not mention the sign of L12. In ternary mixtures of twosolutes diffusing in a solvent medium, cases are known where the couplingcoefficients are negative and coupling can lead to some 25% reduction in theentropy generation rate. It has also been observed that matter can moveagainst its thermodynamic potential gradient, thus causing a negative con-tribution to Sgen. However, in such instances the positive contribution dueto heat flow in the proper direction—namely, of lower temperatures—willmore than compensate for that, thus obeying the second law.

Entropy Generation: Cause and Effect 39

5 LIMITED VALIDITY OF LINEAR LAWS

Linear laws appear to have a limited validity. This may be experienced asimpractical because in that case much more experimental evidence has to becollected for establishing the relation between Ji and Xi, but as we shall seelater, this is also the source for much more excitement in industrial practiceand nature. The validity of linear laws for heat and mass transfer reaches asfar as the phenomenological laws of Fourier and Fick reach. In the case ofFick’s law, the range of validity may be shorter or longer because it is thethermodynamic potential difference, not the concentration difference, that isthe driving force. Similarly, Fourier’s law is based on temperature differ-ences, but the true driving force is D(1/T ) not DT, and again the true rangeof validity is decided by the validity of the linear relationship between theflow rate of heat and D(1/T ).

An interesting case is presented by chemical reactions. For simplicity,we consider an ideal solution in which the molecules M and N participate inthe reaction

M V N ð24ÞTheir steady-state concentrations are maintained such that the chemicalaffinity A, defined by Eq. (4) (AuAM�AN), is positive and thus the chemicalsystem is out of equilibrium. The reaction velocity vch is positive and givenby

vch ¼ v!� v

¼ k!½M� � k

½N� ð25ÞThe rate of lost work is [Eqs. (6) and (11)]

W�lost ¼ T0S

�gen ¼ T0 � A

T� vch ð26Þ

We assume, again for simplicity, that T=T0 and thus

W�lost ¼ A � vch ð27Þ

We now derive the relation between the chemical flow rate vch and itsdriving force A. Earlier we defined

Au AM � AN ð28Þand thus for the equilibrium situation

Aeq ¼ AM;eq � AN;eq ð29Þ¼ 0

Assuming that M and N are present in an ideal solution,

AM � AM;eq ¼ RT0lnð½M�=½M�eqÞ ð30Þ

Chapter 440

with a similar expression for component N. Subtracting Eq. (29) from Eq.(28) results in

A ¼ RT0ln½N�½M�� �

eq

½N�½M�� �" #

ð31Þ

At equilibrium, the chemical velocity vch is zero and thus v! ¼ v

.

This allows us to write

k!½M�eq ¼ k

½N�eq ð32Þand introducing this relation in Eq. (31) we find that

A ¼ RT0lnðk!½M�= k ½N�Þ ð33Þ

¼ RT0 ln v!= v

in which we have assumed that we are close enough to equilibrium that k!

and k

still have their equilibrium values.From Eq. (33) we find

v!= v ¼ expðA=RT0Þ ð34Þ

Remembering that

vch ¼ v!� v

ð35Þ

¼ v!ð1� v

= v!Þ

and introducing Eq. (34) into Eq. (35), we finally obtain the relation betweenvch and A:

vch ¼ v!½1� expð�A=RT0Þ� ð36Þ

According to Eq. (25), v!

is the molar rate of conversion of M into N. Eq.(36) shows that if A/RT0<<1, then vch is linear in A: vch ¼ v

!A=RT0. For

increasing values of A/RT0, the chemical velocity quickly approaches its‘‘saturation’’ value, vch ¼ v

!, which is reached in the limit of A/RT0!l, as

can be seen from Fig. 3.Meanwhile, the rate of lost work is given by Eqs. (27) and (36).

W�lost ¼ A � v! 1� exp � A

RT0

� �� �ð37Þ

To allow an easy interpretation of this equation, we introduce the dimen-sionless properties

y ¼ W�lost

RT0 v! ð38Þ

and

x ¼ A

RT0ð39Þ

Entropy Generation: Cause and Effect 41

and thus Eq. (37) reads

y ¼ xð1� e�xÞ ð40Þ

This equation has two interesting limits (Fig. 4). When x!0, that is,on approaching equilibrium, y!x2, the chemical velocity depends linearlyon the affinity and the lost work rate changes with its square. For x!l,that is, giving in to a highly spontaneous and irreversible reaction, y!x andthe lost work rate depends linearly on the affinity. These results can be readfrom Fig. 4, where Eq. (40) has been plotted. Surprisingly, outside the linearregion, the lost work rate is lower than if the linear region extended over alarger range of affinities, although for larger affinities the lost work rateincreases all the same. Maybe this is unique for chemical reactions.

Now suppose it is possible to convert M into N via a number, n, ofsequential reactions, of which we assume that they have equal rate constants.

MV � � �MiVMjVMk � � �VN ð41Þ

The overall affinity A remains the same, but each step i now has an affinity,on average, of Ai=A/n for each i. In the steady state the chemical reactionvelocity vch is now

vch ¼ : : : vi ¼ vj ¼ vk ¼ : : : ð42Þ

Figure 3 The reaction velocity as a function of the chemical affinity.

Chapter 442

with

vi ¼ v!i 1� exp � A

nRT0

� �� �ð43Þ

The corresponding expression for the rate of lost work in terms of the overallaffinity now reads, in dimensionless units,

y ¼ x 1� exp � x

n

� �h ið44Þ

This equation has been plotted in Fig. 5 for various values of n and wasdiscussed above for n = 1, the spontaneous reaction from M to N withoutany intermediate molecules.

We notice that if we assume an overall affinity A of about 10 kJ, thatis, x = 4, y is about 4 for the spontaneous reaction from M to N (n = 1).However, for n = 4, that is, with three intermediate molecules between Mand N, y, the dimensionless lost work rate, has dropped to a value of 2.5, ornearly with 40%.

Figure 4 The rate of lost work as a function of the chemical affinity (in

dimensionless units; see text).

Entropy Generation: Cause and Effect 43

The lesson to be learned from this rather coarse and simplified analysisis that spontaneous reactions are costly and energy-inefficient. The sponta-neous combustion of fossil fuels for example costs about 30% of the workavailable in the original fuel [3]. Instead one should aim for bridging thedistance in affinity by a limited number of coupled reactions, which aresequential and share a common intermediate.

Lehninger [7] gives some very clear examples of coupled, sequentialreactions with a common intermediate in living systems. As an illustration,we consider the following reactions:

XfPþADP! XþATP ðIÞATPþ Y! ADPþ YfP ðIIÞIn reaction (I), XfP is a biochemical molecule rich in chemical energy

with respect to molecule Y through the attachment of the ‘‘energy-rich’’phosphate group fP. Direct transfer of fP to Y is not possible; it requiresthe common intermediate ATP, adenosine triphosphate. Adenosine diphos-phate, ADP, takes over this fP group first and forms ATP. Next, ATP

Figure 5 The rate of lost work as a function of the chemical affinity and the

number of sequential reactions (in dimensionless units; see text).

Chapter 444

transfers the fP group to Y. In this reaction sequence ATP is the commonintermediate and acts as an energy carrier in the transfer of chemical energyfrom compound X to Y. Both reactions (I) and (II) make use of what we liketo call the downhill–uphill principle: The downhill reaction from XfP toX+fP ‘‘pays’’ for the uphill reaction of ADP and fP to ATP. Thedifference is the work lost in reaction (I), which may be an order smallerthan the chemical energy transferred. The same analysis holds for reaction(II). In this way biochemical reactions seem to proceed less abruptly, lessspontaneously, and more controlled. Chemical energy will have dissipatedall the same, but in many small steps. In this way an impressive complexdynamic and functional structure is sustained that stays out of equilibrium:the living system.

By the way, this is an example of what humans can learn from nature.The great distance in affinity between food molecules and their degradationproducts, which are ultimately recycled and recombined with the help ofwork available in sunlight, appears to be broken up in a lengthy sequence ofreactions coupled by common intermediate molecules [7].

What will happen further away from equilibrium when the linearrelationship between cause and effect breaks down is clear for the aboveexample but for other instances is the subject of much research and specula-tion. With nonlinear relationships the scope of phenomena becomes nearlyunpredictable. Nonlinear dynamics [8, 9] may well provide the clue to thephenomenon of macroscopic complexity [10], a rapidly expanding field ofscience, defined by some [11] as quickly becoming a field of ‘‘perplexity.’’

6 CONCLUSION

Equilibrium and nonequilibrium thermodynamics can be combined to give acomplete thermodynamic description of a process or process step. Equilib-rium thermodynamics allows us to calculate the changes in thermodynamicproperties with the change in process conditions. Nonequilibrium thermo-dynamics allows us to calculate unambiguously the work that is lost asso-ciated with the process taking place. It relates this loss to the process’s flowsand forces driving these flows and identifies the various friction factors as afunction of the relationship between flows and forces.

REFERENCES

1. Katchalsky, A.; Curran, Peter F. Non Equilibrium Thermodynamics inBiophysics, 5th Ed. Harvard University Press: Cambridge, MA, 1981.

Entropy Generation: Cause and Effect 45

2. de Swaan Arons, J.; de Loos, Th.W. Phase Behaviour, Chapter 5. In:Models forThermodynamic and Phase Equilibria Calculations; Sandler, Stanley I., Ed;Marcel Dekker: New York, 1994.

3. Smith, J.M.; Van Ness, H.C.; Abbott, M.M. Introduction to Chemical Engi-neering Thermodynamics, 5th ed. McGraw-Hill: New York, 1996.

4. Bejan, Adrian, personal communication. See also his book, Entropy Genera-

tion Minimization, CRC Press, Boca Raton, FL, 1996.5. Onsager, L. Phys. Rev. 37, 1931, 405; 38, 1931, 2265.6. Prigogine, I. Thermodynamics of Irreversible Processes, 3rd ed; Interscience

Publishers: New York, 1967.7. Lehninger, Albert L. Bioenergetics, 2nd ed; Benjamin/Cummings Publishing

Company: Meulo Park, CA, 1973.

8. Strogatz, S.H. Nonlinear Dynamics and Chaos, with Applications to Physics,Biology, Chemistry and Engineering. Addison-Wesley Publishing Company:Reading, MA, 1994.

9. Guckenheimer, J.; Holmes, P. Applied Mathematical Sciences 42, Nonlinear

Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer:New York, 1997.

10. Nicolis, G.; Prigogine, J. Exploring Complexity, W.H. Freeman: New York,

1989.11. From Complexity to Perplexity, essay in Scientific American, June 1995.

Chapter 446

5Reduction of Lost Work

This chapter establishes a direct relation between lost work and the fluxesand driving forces of a process. The Carnot cycle is revisited to investigatehow the Carnot efficiency is affected by the irreversibilities in the process. Weshow to what extent the constraints of finite size and finite time reduce theefficiency of the process, but we also show that these constraints still allowa most favorable operation mode, the thermodynamic optimum, where theentropy generation and thus the lost work are at a minimum. Attentionis given to the equipartitioning principle, which seems to be a universalcharacteristic of optimal operation in both animate and inanimate dynamicsystems.

1 A REMARKABLE TRIANGLE

The second law in the form that suits us best states that in real processes,and thus in engineering practice, the production of entropy is positive:

_Sgen > 0 ð1ÞBy applying the first and second laws to processes in which heat

and work are exchanged with the environment at P0, T0, we have shownbefore that this generated entropy is associated with a loss of work accord-ing to

_Wlost ¼ T0_Sgen ð2Þ

On the other hand, irreversible thermodynamics has provided us withthe insight that entropy generation is related to process flow rates like thoseof volume, _V, mass in moles, _n, chemical conversion, vch, and heat, _Q, andtheir so-called conjugated forces D(P/T ), -D(A/T ), A/T, and D(1/T ). Al-

47

though irreversible thermodynamics does not specify the relationship be-tween these forces X and their conjugated flow rates J, it leaves no doubtabout the identity of the thermodynamic driving forces Xi and the resultantentropy production rate:

_Sgen ¼Xi

JiXi ð3Þ

The simple conclusion that we can now draw is that the work lost canbe directly related to the process’s flows and driving forces. By eliminating_Sgen from Eq. (2) and (3), we obtain

_Wlost ¼ T0

Xi

JiXi> 0 ð4Þ

So another, more appealing, formulation of the second law is that in areal process available work, exergy, is always dissipated and correlated withthe flows and driving forces of the process. This formulation has beenrepresented in Fig. 1. This figure illustrates how important insights fromClausius, Gouy and Stodola, and Onsager, or from classical, engineering,and irreversible thermodynamics, respectively, show a remarkable interre-lationship. It is not without the second law that Eq. (4) can be obtained, butonce the entropy has been eliminated, this equation seems to be free fromthermodynamics, with the exception perhaps of the definition of thethermodynamic forces. The equation expresses in a ‘‘down-to-earth’’ waythe price that must be paid for energy ‘‘consumption’’ in terms of a process’sflow rates and driving forces.

With Xi’s approaching zero, lost work will approach zero, but thisresult is not very realistic as flows will tend to become zero, too. In practice,we deal with equipment of finite size which we wish to operate in finite time.So the question is what, with these constraints, the minimum amount of lostwork is. Thus it is clear that minimization of lost work and thus of entropyproduction is a challenging subject with many aspects.

Figure 1 The magic triangle relating classical, engineering, and irreversible thermo-dynamics.

Chapter 548

2 CARNOT REVISITED: FROM IDEAL TO REALPROCESSES

We recall that the maximum amount of work available in a heat flow _Q of aconstant temperature TH > T0 is given by

_Wmaxout ¼ _Qin 1� T0

TH

� �ð5Þ

This perfect result can be achieved by operating a Carnot heat enginebetween the temperatures TH and T0 (Fig. 2). In this operation heat isisothermally transferred from the heat source at a temperature TH to aworking fluid, whereas an amount of heat _Qin – _Wout

max = _Q0min is isothermally

transferred from the working fluid to the environment at temperature T0.In reality, however, there is no such thing as isothermal heat transfer.

After all, according to Eq. (13) of Chapter 3, the transfer of a finite amount ofheat requires a finite temperature difference DT, or more correctly, D(1/T). Sothe working fluid of the engine, strictly speaking, operates between THC andT0C, rather than between TH and T0 (Fig. 3). This implies the loss of powerdue to the lost work rate incurred between TH and THC and T0C and T0

according to Eq. (8) of Chapter 3:

_Wlost ¼ _Qin � T0 � D 1

Tð6Þ

The higher _Q in and _Q 0, the higher the required and associatedtemperature differences for heat transfer into the working fluid at hightemperatures and out from the working fluid at low temperatures for heatexchangers with finite heat exchange area. If the assumption is made thatthese two losses during heat transfer are the only sources of irreversibility, of

Figure 2 The Carnot engine operating between TH and T0.

Reduction of Lost Work 49

lost work in the Carnot cycle, we speak of endoreversibility, expressing thatthe Carnot cycle itself does not incur further losses in the power-producingand consuming devices of the power cycle.

The analysis of this endoreversible engine shows a remarkable resultthat was independently obtained by a number of researchers [1]. Two speciallimit cases can be identified. The first case is the limit where _Qin! 0 and thus_Wout ! 0, point 1 in Fig. 4. Heat is thus infinitely slowly, reversibly,extracted from the heat source and transferred to the engine. The efficiencyof the engine is the Carnot efficiency of an engine operating between TH andT0: D = 1 – T0/TH because THC = TH and T0C = T0 in this limit case. Theother limit case is point 2 in Fig. 4, in which the rate at which heat istransferred into the cycle has reached a maximum and all its available workis dissipated between the temperature TH and THC and T0C and T0 withTHC = T0C. Work originally available in the heat flow driving the engine is

Figure 4 Power output _Wout and efficiency D as a function of the heat flow rate _Qin.

Figure 3 The endoreversible Carnot engine operating between THC and T0C.

Chapter 550

leaking away through the heat engine to the environment at T0, whereas inthe former limit all available work was leaking away outside the engine tothe environment.

Thus there should be an optimum rate _Qin, point 3 in Fig. 4, for whichthe power output of the engine _Wout has a maximum. This so-calledmaximum power is achieved for two optimal temperatures THC

opt and T0Copt

related to the two original temperatures TH and T0 according to

T opt0C

T optHC

¼ffiffiffiffiffiffiffiT0

TH

rð7Þ

The corresponding thermodynamic efficiency is given by

D ¼ 1� T opt0C

T optHC

¼ 1�ffiffiffiffiffiffiffiT0

TH

r ð8Þ

For a proof of this result, we refer to the original papers [1,2], but wecan make the existence of these two optimal temperatures plausible by thefollowing reasoning. Suppose we wish to introduce heat into the Carnotengine with a rate _Qin. This fixes the upper temperature THC of the Carnotcycle, for example by the approximate relation

_Qin ¼ ðkAÞHðTH � THCÞ ð9Þin which k and A represent the overall heat transfer coefficient and heattransfer area, respectively. THC, in turn, fixes the lower temperature T0C ofthe Carnot engine. After all, for a Carnot engine the heat taken in and theheat rejected are related according to

_Qout

_Qin

¼ T0C

THCð10Þ

which in our case can be rewritten as

ðkAÞLðT0C � T0ÞðkAÞHðTH � THCÞ ¼

T0C

THCð11Þ

It is obvious from Eq. (9) that by fixing _Q in, THC is fixed and thataccording to Eq. (11) this fixes T0C. The power of the engine is then given by

_Wout ¼ _Qin 1� T0C

THC

� �ð12Þ

Reduction of Lost Work 51

Varying _Q in between the two extremes of points 1 and 2 shouldproduce an optimal value _Qin

opt for which _Wout is a maximum, as shown inFig. 4. This maximum power corresponds to optimal values for the temper-atures between which the Carnot engine operates, THC and T0C. Theseoptimal values are related to TH, the temperature at which heat is madeavailable and T0, the temperature of the environment that acts as the heatsink for the heat rejected by the engine. By maximizing _W with respect toTHC, we can find Eqs. (7) and (8).

Thus, for a heat engine operating reversibly between T0 = 288 K andT = 775 K, the Carnot efficiency is 0.63, whereas the efficiency of theendoreversible engine considered at maximum power is 0.39, a result thatshows remarkable agreement with the observed results for real powerstations.Curzon and Ahlborn report in their original paper [2] on the efficiencies ofthree powerstations in the U.K., Canada, and Italy. The observed efficiencieswere respectively 36%, 30%, and 16%, whereas calculation with Eq. (8) gaverespective values of 40%, 28%, and 17.5%. The Carnot efficiencies were64.1%, 48%, and 32.3%, respectively. The thermodynamic efficiency of theengine as function of _Qin is also plotted in Fig. 4 and moves from its Carnotvalue at _Qin = 0 to the value zero for maximum heat throughput.

The impression may be given that operating at maximum powercannot take place at the most favorable conditions, namely at the minimumentropy generation rate. But as Bejan subtly shows [3] the conditions formaximum power must be the conditions for the minimum entropy gener-ation rate, completely in line with what one would expect from the Gouy-Stodola relation, Eq. (12) of Chapter 3. In essence, we need to identify thecontributions to the entropy generation rate. The first contribution is thatfrom the heat exchanger at the high-temperature end of the Carnot engine:

_Sgen;1 ¼ _Qin1

THC� 1

TH

� �ð13Þ

The second contribution is that from the heat exchanger at the low-temperature end of the engine:

_Sgen;2 ¼ _Qout1

T0� 1

T0C

� �ð14Þ

The third contribution is from the original heat flow _Qsource after it hastransferred part of its heat, _Qin, to the engine. Suppose this flow _Qsource is asaturated vapor, condensing at TH to an extent that depends on the heat _Qin

that has been drawn into the engine. After leaving the heat exchanger, theheat flow ( _Q source – _Q in) will exchange heat with the environment at T0,

Chapter 552

resulting in the third contribution to the entropy generation rate, _Sgen,3 =( _Qsource – _Qin)

1T0� 1

TH

� �. The total entropy generation is then

_Stotalgen ¼ _Sgen;1 þ _Sgen;2 þ _Sgen;3 ð15Þ

Minimizing _Sgentotal with respect to THC or T0C will result in the same

optimal values for _Q in, THC, and TLC, and the same value for maximumpower. This minimum value is, positioned at point 3, Fig. 5, between the twoextreme values of _Sgen

total in points 1 and 2, respectively. In point 1 the engineoperates so slowly that all the work available in the original heat flow isdissipated outside the engine: _Sgen,1 and _Sgen,2 are both zero and _Sgen,3 is at itsmaximum value. In point 2 again all the originally available work isdissipated, the entropy generation rate in the heat exchangers is maximumas THC = T0C. In both 1 and 2 all heat originally available at TH has beentransferred to the environment, producing the maximum possible entropygeneration.

In conclusion, an optimum heat flow rate _Qinopt can be found (Fig. 4)

between a zero rate and a maximum rate of _Q in. At zero rate the engineoperates at maximum, Carnot, efficiency but without output of workbecause of the infinitely low rate. All the work available at the source leaksaway into the environment, that is, outside the engine. At the maximum rateof _Qin the yield is zero again because all available work is leaking throughand outside the system. For the optimum rate in between these rates, thepower output is at a maximum and causing the least dissipation of work andgeneration of entropy: at maximum power output, the entropy generationrate is at a minimum.

Finally, we want to point out that the concept of the endoreversibleengine is a simplification that leads to a quick and clear insight into the role

Figure 5 Entropy generation rate as function of the heat flow rate.

Reduction of Lost Work 53

and thermodynamic cost of transfer processes in reducing the Carnotefficiency into smaller and more realistic values. But for finding the realoptimum conditions, the concept of endoreversibility has to be sacrificed.This will complicate the matter to some extent but will allow for includingall contributions to lost work:

_Wlost ¼ T0

Xi

JiXi ð16Þ

thus providing a complete insight into all sources of dissipation and theirrelative contributions.

Note: The transfer of heat, mass, and momentum seems to receive themost attention in textbooks on transport phenomena. However, the transferof chemical energy, for example, by coupled reactions, of which bioenergeticsprovides many examples [4] is another interesting topic. We have shown [5]that living systems appear to operate as conductors for chemical energy,whereby, in a way of speaking, energy permeates the system to wherever it isrequired. Hill [6] launched the term ‘‘free energy transduction.’’From a closerlook at this process, we can learn that via coupled chemical reactions, that is,themechanism of downhill reactions driving uphill reactions, chemical energyis transported through the system. Every coupled reaction has, of course, itsloss despite its, usually high, thermodynamic efficiency (>90%). In the end allwork originally available in food will be dissipated. In themeantime the livingsystem is kept in a dynamic,most often, steady state out of equilibriumwith itsenvironment, which is the very essence of life. His efforts to understand thisfrom thermodynamic principles resulted in Erwin Schrodinger’s famousmonograph, What Is Life? [7].

3 FINITE TIME, FINITE-SIZE THERMODYNAMICS

The analysis given in Section 5.2 is very revealing. Let us go over thehighlights again. There is a source of heat available at a temperature TH andat a fixed rate _Qsource. This fixes the amount of work available at the sourceper unit time. The largest fraction of this work that can be obtained asmaximum power output, _Wout

max, is realized for an optimal value of _Qin, therate at which heat is transferred from the source to the endoreversibleCarnot cycle. The other part, _Qsource – _Qin

opt, leaks away to the environment,_Qleakage. If _Wout

max is the so-called rated power of the powerstation, this meansthat a finite amount of work has to be produced in a finite time. An optimalvalue of _Qin

opt takes care of this with _Qinopt = (kA)H (TH – THC

opt). The optimalvalue for the upper temperature of the Carnot engine, THC

opt, follows fromthis relation, given the overall heat transfer coefficient k and the finite size of

Chapter 554

the heat exchanger, namely the area of the heat transfer. The choice of othermaterials will of course affect the outcome.

We believe that finite-size, finite-time thermodynamics has a significantdidactic value. The unrealistic limit of the Carnot or reversible cycle isreplaced and a more realistic presentation of actual processes is obtained bycombining the results of equilibrium thermodynamics with those of irre-versible thermodynamics, which is more concerned with the rate and drivingforces of processes.

4 THE PRINCIPLE OF EQUIPARTITIONING

In 1987 Tondeur and Kvaalen [8] drew attention to an important principlethat they proved to be valid in the linear region of irreversible thermodynam-ics but that they expected to have a wider application. Discussing heat,momentum, and mass transfer, they stated that given a specified transferduty and transfer area, the total entropy generation rate is minimal when thelocal rate of entropy generation is uniformly distributed, equipartitioned,along the space and time variables of the process. Some 10 years later, in 1998,Bejan and Tondeur [9] identified this principle as a universal design principlethat accounts for the macroscopic organization in nature both in inanimatesystems, such as rivers, as in animate systems, such as trees. They showed thatthe optimal performance of a finite-size system with purpose is alwayscharacterized by the equipartition of driving forces or even of the materialrequired for process equipment, for example, heat exchangers, over theprocess. Bejan gives a series of examples of this remarkable principle [10].

To illustrate this principle, we choose the simplest possible example.Suppose the purpose of our process is to heat a flow of mass in a finite timesuch that its temperature increases with DT. This requires a heating duty of

J ¼ _mcpDT ð17Þwith _m the mass flow rate and cp the specific heat at constant pressure. Forthis process we choose the heat exchanger as the equipment and identifybetween the heating and heated flow the local heat flux j and conjugate forcex = D(1)/(T) (see Fig. 6). We assume a linear relationship between flux andforce: j = kx. The local entropy generation rate is thus _sgen = jx. We maynow write

J ¼Z

A

jdA ¼ k

ZA

xdA ð18Þ

and

_Sgen ¼Z

A

_sgendA ¼ k

ZA

x2dA ð19Þ

Reduction of Lost Work 55

in which A represents the heat transfer area. We impose the constraint offinite size by putting A constant and ask ourselves what the optimaldistribution is of the force x over the heat exchanger. Therefore, we seekthe solution to the above equations in terms of the distribution of x thatmakes _Sgen minimum. With the help of variational calculus [7], we find

x ¼ D1

T

� �Local

¼ constant ð20Þ

As a result, j and _sgen are constant as well. Local fluxes, forces, andentropy generation rates are equipartitioned or evenly distributed over theheat exchanger. In this way we have obtained a realistic minimum for the lostwork rate in this process, a minimum associated with the duty of the process,the finite size of the equipment, and the finite time in which the process has tobe carried out. This is a splendid example of thermodynamic optimization,providing us with the optimal distribution of the driving force of the processfor the most efficient operation under the set constraints. In a real heatexchanger it will be difficult to design for this distribution, but it can beapproached in a countercurrent heat exchanger, which is far more efficientthan the co- or cross-current heat exchanger. This is visualized in Fig. 7, whichcompares the rate with which work is lost (represented by the enclosed areas;see Fig. 2. in Chapter 3) in a countercurrent and a co-current heat exchangerwith specified mass flow rates, specific heats, and inlet temperatures.

It is plausible from comparing these figures that the co-current con-figuration of the heat exchanger generates more entropy than the counter-current configuration. Tondeur and Kvaalen [8] have generalized thetheorem to the simultaneous transfer of mass, momentum, and heat, againunder the restriction of the validity of linear laws and Onsager’s relations of

Figure 6 Local heat flux j and driving force x =D(1/T) in a heat exchanger. The

temperature increase of the cold stream is DT.

Chapter 556

reciprocity. They also discuss how this theorem can be incorporated in theeconomic analysis of the process, but this subject is beyond the scope of thisbook and is left to the reader for further investigation. For a more thoroughdiscussion and for some other illustrative examples of this principle, we referto the original papers [8,9].

Bejan and Tondeur [9] make a number of other observations in theirpaper. One is that the relation between j and x is not necessarily linear.Another observation is that a similar analysis can show that the force xshould be equipartitioned in time, which is another way of saying that thesteady state is optimal. An earlier proof of this principle was given byPrigogine [11]. The steady state is common in nature and often the favoredstate in industrial operation. It can be considered to be the ‘‘stable state’’ ofnonequilibrium thermodynamics, comparable to the equilibrium state ofreversible thermodynamics (see Fig. 2, Chapter 4). Of course, the latter ischaracterized by _S gen = 0, whereas the former is characterized by aminimum value _S gen

min, larger than zero. A disturbance of this stable anddynamic state will incur an increase of the entropy generation rate only tomake it fall back to its minimum value. The stability condition therefore is

d _Sgen

dt< 0 ð21Þ

5 CONCLUSIONS

The ideal, un-realistic, but basic limit of the thermodynamic efficiency of aprocess is that of the reversible process where all work available and

Figure 7 (a) Co-current versus (b) countercurrent heat exchange between the sameinlet temperatures TH and TL.

Reduction of Lost Work 57

entering the process is still available after the process. Work has simply beentransferred from one carrier to another. Driving forces are infinitesimallysmall and the process is ‘‘frictionless’’: no barriers have to be taken. As aresult there is no entropy generation nor loss of available work. The workrequirements of the process can be accurately calculated from the thermo-dynamic properties of the equilibrium states that the process passes through.

For the establishment of the realistic limit, one has to take account ofthe rates of processes in which mass, heat, momentum, and chemical energyare transferred. In this so-called finite-time, finite-size thermodynamics, it isusually possible to establish optimal conditions for operating the processnamely with a minimum, but nonzero, entropy generation and loss of work.Such optima seem to be characterized by a universal principle: equiparti-tioning of the process’s driving forces in time and space. The optima mayeventually be shifted by including economic and environmental parameterssuch as fixed and variable costs and emissions. For this aspect, we refer toChapter 18.

REFERENCES

1. Bejan, A. Entropy generation minimization: The new thermodynamics of finitesize devices and finite time processes. Appl. Phys. Rev. 1, Feb.1996, 79(3).

2. Curzon, F.L.; Ahlborn, B. Am. J. Phys. 1975, 43, 22.3. Bejan, A. Entropy Generation Minimization; CRS Press: Boca Raton, FL, 1996.

4. Lehninger, A.L. Bioenergetics, 2nd Ed; W.A. Benjamin Inc.: Menlo Park, CA,1973.

5. Lems, S.; van der Kooi, H.J.; de Swaan Arons, J. Thermodynamic optimization

of energy transfer in (bio)chemical reaction systems. Chem. Eng. Sc. May 2003,58 (10), 2001–2009.

6. Hill, T.L. Free Energy Transduction and Biochemical Cycle Kinetics; Springer-

Verlag: New York, 1989.7. Schrodinger, E. What Is Life? Cambridge University Press: Cambridge, U.K,

2000.8. Tondeur, D.; Kvaalen, E. Equipartition of entropy production. Ind. Eng.

Chem. Res. 1987, 26, 50–56.9. Bejan, A.; Tondeur, D. Equipartition, optimal allocation, and the constructal

approach to predicting organization in nature. Rev. Gen. Therm. 1998, 37,

165–180.10. Bejan, A. Shape and Structure, From Engineering to Nature; Cambridge

University Press: Cambridge, U.K, 2000.

11. Prigogine, I. Introduction to Thermodynamics of Irreversible Processes, 3rd Ed.Interscience Publishers: New York, 1967.

Chapter 558

6Exergy, a ConvenientConcept

He who would learn to fly one day must first learn to stand and walkand run and climb and dance. One cannot fly into flying.

—F. Nietzsche

In this chapter we make preparations for performing a thermodynamicanalysis of a process. The principles of such an analysis are defined first.From the calculation of the minimum, also called the ideal amount of workto perform a certain task, the convenience, not the necessity, of definingthe concept of exergy is made plausible. Exergy can have a physical and achemical component. The quality of the Joule is another convenient conceptfor a clear analysis and for conclusions on process performance.

1 EXERGY

In view of the presentation of material in Part I, we can state that every taskthat we set ourselves in industry implies lost work. This holds for processesproducing work equally well as for those requiring work. The challenge is tounderstand the nature of this lost work and from there to apply originalityand intelligence to reduce it.

In the following we deal with a steady-state flow process and considera flow originally at ambient conditions, P0 and T0, and requiring work at therate _Win to bring its conditions at P and T (Fig. 1). In the process heat istransferred to the environment at a rate of _Qout.

As is justified for most situations in process technology, we ignoremacroscopic changes in the kinetic and/or potential energy of the flow in

59

this process. Applying the first law of thermodynamics for flow processes,we may write

_Win ¼ _mDHþ _Qout ð1ÞThe second law for this process reads

_Sgen ¼ _mDSþ _S0 ð2Þin which _S0 denotes the rate of the change in entropy of the environment.

Next we wish to establish the minimum amount of work to accomplishthe change in the flow’s conditions from P0, T0 to P, T, that is, to bringabout the corresponding changes in the state properties H and S of the flow,DH and DS, with

DH ¼ HP;T �HP0;T0ð3Þ

and

DS ¼ SP;T � SP0;T0ð4Þ

We will therefore rewrite Eq. (1) as

_W minin ¼ _mDHþ _Qmin

out ð5Þor even

_W minin ¼ _mDHþ _Qmin

0 ð6ÞBy writing _Q0

min for _Qoutmin, we want to emphasize that the heat released to the

environment must have no potential left, in order to assess the true mini-mum for _Win. The minimum rate of input of work is associated with theminimum output of heat, as _mDH is fixed by the choice of the mass flow rate

Figure 1 Work and heat exchange with the environment when a flow is broughtfrom P0, T0 to P, T conditions.

Chapter 660

and the thermodynamic conditions of the initial state and the final state.Next we combine Eqs. (2) and (6), replacing _Q0

min by applying the relation

_Qmin0 ¼ T0

_S0 ð7Þand find

_W minin ¼ _mðDH� T0DSÞ þ T0

_Sgen ð8ÞThe true minimum will, of course, require that the process is free of drivingforces, thus that

_Sgen ¼ 0 ð9ÞThe minimum amount of work to bring about the required change inconditions appears then to be given by

_W minin ¼ _mðDH� T0DSÞ ð10Þ

We can now define the property exergy, Ex, according to

Ex u_W min

in

_m¼ ðHP;T �HP0;T0

Þ � T0ðSP;T � SP0;T0Þ

ð11Þ

as the amount of useful work confined in a unit of mass of the flow atconditions P and T with respect to the conditions of the environment. It isthe maximum amount of work that a unit mass of flow can perform if it isbrought reversibly to the conditions of the environment. We may rewriteEq. (11) as

Ex ¼ ðH� T0SÞP;T � ðH� T0SÞP0;T0ð12Þ

In American literature [1] the term H � T0S is often indicated as theavailability function BuH � T0S, which stems from the concept ‘‘avail-able’’ work. This should not suggest, as it sometimes occurs in literature,that exergy is the same as availability. It is not, because from Eq. (12) itfollows that

Ex ¼ BP;T � BP0;T0ð13Þ

At P0T0 the exergy will be zero according to our definition, but this does notimply that BP0T0

= 0. On the contrary, as

BP0;T0u ðH� T0SÞP0;T0

¼ GP0;T0ð14Þ

the availability function at environmental conditions can be identified as theGibbs energy at these conditions. As one can easily verify, this property is

Exergy, a Convenient Concept 61

not determined as it contains enthalpyH and therefore the internal energy Uas a property of unknown absolute magnitude. The zero level has often beenarbitrarily chosen, albeit for good reasons. In the case of water, the meltingpoint is the zero level for liquid water’s enthalpy. With the exception for theconditions P0T0, the availability expression at P and T

B ¼ H� T0S ð15Þshould not be mistaken for the value of the Gibbs energy G at P and T.

If the flow is brought from conditions P1, T1 to P2, T2 without achange in its composition, we may write

DEx ¼ Ex2 � Ex1 ð16ÞDEx is the minimum amount of work to bring about the indicated changesin thermodynamic conditions. The terms on the right-hand side of Eq. (16)represent the maximum amount of work that the unit mass of flow canperform if the flow is reversibly brought back from states 1 and 2,respectively, to the pressure P0 and temperature T0 of the environment.

2 THE CONVENIENCE OF THE EXERGY CONCEPT

With the definition of exergy it has become possible to assign to a stream aquality in terms of the potential to perform work. While lost work is depen-dent on the specific process that we perform to accomplish a certain goaland varies with the way the process is performed, exergy is, in contrast, anunambiguous property fully defined as a state property as soon as the con-ditions of the unit mass of flow and those of the environment are defined.*As exergy has been defined purely in terms of work, an exergy balancearound a process, including its interaction with the environment, shouldresult in an exergy loss that is precisely the amount of lost work, thus

Exin � Exout ¼ Exlost

¼Wlost

ð17Þ

Determination of the amount of lost work does not require the introductionof the concept of exergy. With the definition of Eq. (10), the overall DH andDS decide on the amount of minimum work required to bring about thechange in conditions. More work brought into the process than is strictly

* Other forms of exergy can be those associated with kinetic and potential energy, which we

have neglected in this treatment.

Chapter 662

necessary according to Eq. (10) must have been the work dissipated onovercoming the process ‘‘frictions.’’

Equation (10) led to the definition of exergy, whereas the sameexpression in Eq. (20) of Chapter 3 does not. Both equations express theminimum amount of work to transform the conditions of a defined amountof mass from those in state 1 into those of state 2. But if we choose state 1 asthat of the environment, the environment suddenly acts as the datum levelfor a property of the amount of mass considered. The simplest example wecan think of is air. Ignoring for the moment other constituents than nitrogenand oxygen, air at environmental conditions P0T0 is ‘‘powerless’’ to performwork for us. According to Eq. (12) its exergy is indeed zero. Air at P = 10bar and T = T0, however, has an exergy value different from zero becauseH � H0 = 0 (ideal gas) and S � S0 = �R ln P/P0 = �R ln 10. Therefore,Ex = RT0 ln 10 and thus about 6 kJ/mole. Indeed, 1 mole of air at 10 barshould, potentially, be able to perform work for us living in an environmentof 1 bar. This is at most the amount of work calculated and is called theexergy of air at 10 bar and ambient temperature. Reversely, it will require atleast this amount of work to transform air from ambient conditions P0T0

into air at 10 bar and ambient temperature. This is exactly the purpose ofintroducing the concept of exergy: expressing the amount of work availablein an amount of mass, in rest or flowing, to perform work if it prevails atconditions different from those of the environment. This simple examplemay suggest that the exergy, at ambient conditions of an amount of naturalgas, for simplicity to be considered as methane only, is also zero. Indeed,applying Eq. (12), we arrive at an exergy value of zero. But this calculationhas only accounted for differences in physical conditions of methane withrespect to the environment—pressure and temperature. Of course, thechemical composition of methane is strikingly different from that of theenvironment, and that is, indeed, the reason why methane is so popular andis needed as an ‘‘energy source.’’ More correctly, this source of exergy is ofchemical origin. By combustion with one component of the environment,oxygen, it can be converted into two other components of the environment,CO2 and H2O, and this reaction is widely used as the source of ‘‘energy.’’ Infact, some expect natural gas to be the fuel of the 21st century. Therefore, wedistinguish between physical exergy and chemical exergy as

Ex ¼ Exphys þ Ex0chem ð18Þ

The first term on the right-hand side of this equation expresses the amountof work available due to differences in pressure and temperature with theenvironment. The second term, the chemical exergy, expresses the amount ofwork available due to the differences in composition with respect to the

Exergy, a Convenient Concept 63

environment. The superscript in Ex0chem expresses that the chemical exergy isconsidered at ambient conditions.

Table 1 lists exergy values for methane. It is clear from this table thatmethane carries an impressive amount of exergy as chemical exergy. Fur-ther, the table shows (1) the influence of increased pressure and temperatureon the physical exergy and (2) that this latter contribution of exergy is nearlytwo orders smaller than the chemical contribution. Chemical exergy is theexclusive subject of Chapter 7.

3 EXAMPLE OF A SIMPLE ANALYSIS

We would like to illustrate the concept of exergy with a simple illustration.We borrow this example from Sussmann [2] because we can hardly think ofa nicer and clearer illustration. Figure 2 illustrates how a stream of 1 kgsec�1 of liquid water at 0jC is adiabatically mixed with a second stream of 1kg sec�1 of liquid water at 100jC to produce a stream of 2 kg sec�1 of liquidwater. The task at hand is to provide a thermodynamic analysis or exergyanalysis of this process. The temperature of the environment is 25jC.

The analysis requires the calculation of three exergy flow rates, at 0,50, and 100jC. As no heat or work is transferred between the considered

Table 1 Exergy Values of Methane (kJ/mole)

P (bar) T (jC) Exph Exch Ex

1 25 0.0 831.6 831.6

100 25 11.0 831.6 842.6100 100 11.3 831.6 842.9

Figure 2 Flow diagram for the mixing of a hot and a cold stream.

Chapter 664

system and its environment, the first law, Eq. (1), yields that the overallenthalpy change is zero:

_m3H3 � _m1H1 � _m2H2 ¼ 0 ð19ÞThe mass balance dictates that

_m3 ¼ _m1 þ _m2 ð20ÞMultiplying Eq. (20) with H0, the enthalpy of liquid water at T0, and sub-tracting the result from Eq. (19), we obtain

_m3ðH3 �H0Þ ¼ _m1ðH1 �H0Þ þ _m2ðH2 �H0Þ ð21ÞAs the change of enthalpy with pressure under these conditions can beneglected and, to some approximation, the specific heat of liquid water canbe considered constant in this example, we can write

Hi �H0 ¼ cpðTi � T0Þ ði ¼ 1; 2; 3Þ ð22ÞIntroducing this relation into Eq. (21) gives us the temperature T3 of theflow leaving the mixer: T3 = 323.15 K. The exergy flow rates can now becalculated from

_Exi ¼ _mi½ðHi �H0Þ � T0ðSi � S0Þ� ð23ÞThe enthalpy term is taken care of by Eq. (22), and the entropy term can becalculated from Eq. (14) of Chapter 2, resulting in

Si � S0 ¼ cplnTi

T0

� �ð24Þ

where we have made the same assumptions as for arriving at the enthalpyterm in Eq. (22). The results are presented in the so-called Grassmannexergy flow diagram (Fig. 3).

Figure 3 Exergy flow diagram or Grassmann diagram for the example of Fig. 2.

Exergy, a Convenient Concept 65

The diagram clearly shows the ‘‘value’’ of each flow in terms of itsability, or potential, to perform work. The diagram also shows that a consid-erable amount of the exergy flowing into the system is dissipated as a resultof the mixing process. However, exergy values are not required to calculatelost work. We could have calculated the same value from

_Wlost ¼ T0_Sgen ð25Þ

with

_Sgen ¼ _m3S3 � _m1S1 � _m2S2 ð26Þwhich can be transformed into

_Sgen ¼ _m3ðS3 � S0Þ � _m1ðS1 � S0Þ � _m2ðS2 � S0Þ ð27Þallowing the calculation of _Sgen and thus of _Wlost directly bymaking use of Eq.(25). However, although _W lost is directly related to the loss of energyresources, its value does not put the process in perspective. Exergy analysisemphasizes the value of the flows and thereby shows the efficiency of theprocess in terms of

g ¼_Exout_Exin

¼ 0:216 ð28Þ

So nearly 80% of the original exergy is wasted in the process, which finds itsorigin in the temperature difference of 100jC between the flows entering theadiabatic mixer. This difference reduces to close to 0jC in the mixing pro-cess. Equation (8) of Chapter 3 explains the resulting work lost in the pro-cess. Reducing the loss is rather senseless in this case as the introduction ofCarnot engines would not be worth the effort, so it seems. This observationgets another dimension, however, if one realizes that in a country like TheNetherlands nearly every citizen starts his or her day by taking a shower withwater that is a mixture of tap water and water from a gas-fed boiler. Theamount of exergy entering the process is then even (much) higher than in ourexample, reducing the efficiency to D = 0.03, or 3%. Losses on this scalewarrant innovative measures, such as discussed in the next example inSection 5 and in Chapter 9.

4 THE QUALITY OF THE JOULE

Earlier we mentioned that the first law deals with the quantity of energy, andthe second law deals with the quality of energy. Looking at the system andits environment at the same time, we see that the first law expresses that for a

Chapter 666

real process the total number of Joules involved remains unchanged. Thesecond law expresses that their quality declines. The total amount ofexergy—available work—dissipates in every process due to irreversibilitiesin the process. It would be nice if we could assign a quality to the Joule,expressing to what extent the Joule concerned has work available. This‘‘quality’’ q with the dimension J/J should have a value 0 V q V 1. We returnto Fig. 4 of Chapter 3 and Fig. 1 here and write

Win ¼ DHþQ0 ð29ÞWe rewrite this equation as

Win �Q0 ¼ DH ð30ÞThis equation expresses that the net energy transferred into the system isapparently stored in the system’s enthalpy. So DH reflects the system’senergy intake in its interaction with its environment. The same equation canbe rearranged, by combining the first and second laws into

Win ¼ DH� T0DSþ T0Sgen ð31ÞFrom this equation we established the earlier minimum for the amount ofwork, the ideal work, required to change the system’s conditions from state1 to 2 with DP = P2 � P1 and DT = T2 � T1 and thereby its thermo-dynamic properties DH = H2 � H1 and DS = S2 � S1:

W minin ¼ DH� T0DS ð32Þ

The real amount of work required exceeds this amount by

Wlost ¼Win �W minin

¼ T0Sgen

ð33Þ

Equation (32) provides the definition of exergy if state 1 is chosen as thestate at ambient condition, namely P1 = P0 and T1 = T0: the minimumamount of work required to transfer the system from environmentalconditions to those at P2 and T2. At these conditions this is the maximumamount of work available for the reverse process. That is the valuable ideabehind the exergy concept: to be able to assign to any process stream avalue, its exergy, that expresses the confined work available in the stream.For the general change in state from P0, T0 to P, T, we can write the netenergy input as

Ennetin ¼ DH ð34Þwhereas the work potential is given by

Ex ¼ DH� T0DS ð35Þ

Exergy, a Convenient Concept 67

From this it follows that every Joule that has entered the system has aquality defined as

q uEx

Ennetin

¼ 1� T0DS

DHð36Þ

Table 2 lists the quality of the Joule for various energy carriers, from air inthe environment to the Joule in hot combustion gases. The table illustratesthat the chemical Joule brought in by methane has suffered in quality fromthe spontaneous reaction of burning the fuel to its combustion gases. It alsoillustrates the value of so-called waste heat if we take into consideration thequality of the Joule that we need for human comfort in the house via hotand warm water. We must emphasize that its meaning is lost as soon as thetemperature falls below that of the environment. Nevertheless, in Chapter 9,which deals with the exergy analysis of energy conversion processes forproducing work, we frequently use this concept for illustrative purposes.

5 EXAMPLE OF THE QUALITY CONCEPT

Figure 4 pictures the case of a natural gas-fired power station. The hotcombustion gases drive a combined cycle consisting of a gas turbine and asteam powerplant. The power station ‘‘cogenerates,’’ or produces, electricityand heat. The produced heat and electricity are used to upgrade the qualityof water in the environment by raising its temperature. We wish to comparethis process with the case where hot water is produced by direct combustionof the gas in a boiler.

The Joules brought into the system originate in the chemical energy ofmethane. We consider 10 Joules, Enin = 10, and follow the fate of these 10Joules with the first and second laws. From process data it follows that 5Joules end up in electricity and 4 Joules in hot water. One Joule finds its waythrough the chimney. The 5 Joules of electricity increase the temperature of

Table 2 The Quality of the Joule (fractionavailable for work in J/J; T0=288.15 K)

Chemical f1Hot combustion gases 0.6–0.8

Waste heat 0.2–0.3Chimney gases 0.2Hot water (100jC) 0.12

Warm water (50jC) 0.06

Chapter 668

water of ambient conditions to that of hot water by means of a heat pump;based on the efficiency of this heat pump, 10 Joules are withdrawn from theenvironment and 15 Joules of hot water are the result.

Let us now follow this process in more detail with the second law andmake use of the quality concept. To keep things simple, we make use of asimplified version of Eq. (36):

qi ¼ 1� T0lnðTi=T0ÞTi � T0

ð37Þ

which results from Eq. (36) by assuming cp as a constant. By definition, thequality of Joules in electricity is unity, as theoretically electricity can be fullyconverted into work. As we shall see in Chapter 7, the quality of Joules innatural gas is approximately unity as well. The quality of the Joules in thechimney gases and in the hot water has been calculated by means of Eq. (37)and is found to be 0.20 and 0.12, respectively. This allows a simultaneousanalysis of the energy and its quality in the alternative process: theproduction of hot water directly from the combustion of natural gas. Forthe latter the exergetic efficiency can be calculated according to (9 � 0.12)/(10 � 1) = 0.11 because 10 Joules of fuel have been transformed into 9Joules of hot water (see Table 2), and 1 Joule exits through the chimney. Forthe cogeneration process, the efficiency is calculated as (19 � 0.12)/(10 � 1)= 0.23, where we have neglected the exergy of the chimney gases, since theseare not used to heat the water. Figure 5 summarizes the results.

The exergetic efficiency of the combustion has been calculated to beD= 0.78, or 78%. For this calculation we used Eq. (36), as we have assumedconditions given by C�engel [3] for the inlet gases of turbines, namely, 1150jCand 14 bar (see Chapter 9 for a similar calculation). This higher pressure willnot affect DH. According to Eq. (14) for the dependence of the entropy onpressure for ideal gases, this term has to be included. The exergetic efficiency

Figure 4 Natural gas-driven cogeneration powerplant for the production of elec-tricity and hot water.

Exergy, a Convenient Concept 69

of the cogeneration step is (5 � 1 + 4 � 0.12)/(10 � 0.78) = 0.70, or 70%,in which we have considered the exergy content of the chimney gases to belost. The thermodynamic efficiency of the entire cogeneration plant is thus0.78 � 0.7 = 0.55, or 55%, a result only achieved in the most advancedpowerplants [3]. The thermodynamic efficiency of the heat pump has beencomputed from (15 � 0.12)/(5 � 1) = 0.36.

The exergetic efficiency of the cogeneration process including the heatpump, Dex = 0.23, appears to be more than twice that of the direct com-bustion process, Dex = 0.11. So this is a 100% improvement in efficiency. Wenote that the exergetic efficiency of the heat pump is 0.36. If the qualityaspect of the Joule were not considered and thus all Joules would beconsidered equal, which they are numerically but not in quality, then theefficiency of the heat pump could be interpreted as 15/5, or 300%. Suchcalculations can be very misleading, and therefore we believe that both theexergy and the quality concept are instrumental in improving communica-tion among everybody involved and concerned. In this context we wish torefer to the quote that we give in Chapter 3 on the quality and quantity ofenergy and the need to make this distinction in policy decisions.

6 CONCLUSIONS

Exergy is a convenient concept if one wishes to assign a quantitative qualitymark to a stream or a product. This quality mark expresses the maximum

Figure 5 Thermodynamic analysis in terms of quality, quantity, and efficiency.

Chapter 670

available work or potential to perform work because of its possible differ-ences in pressure, temperature, and composition with the prevailing envi-ronment. The physical exergy, Exphys, only accounts for the differences inpressure and temperature; the standard chemical exergy, Ex0chem, accountsfor the difference in composition with the environment at the environment’spressure and temperature. Thus

Ex ¼ Exphys þ Ex0chem ð38ÞThe convenience of the exergy concept houses the possibility to discussenergy issues on a clear and quantitative basis, in particular if the exergyvalues assigned to process streams are combined with exergy losses incurredin the processes in which these streams participate, either actively orpassively, as the next chapter illustrates.

REFERENCES

1. Seader, J.D. Thermodynamic Efficiency of Chemical Processes; MIT Press: Cam-bridge, MA, 1982.

2. Sussman, M.V.Availability (Exergy) Analysis; Mulliken House: Lexington, MA,1980.

3. C�engel, Y.A.; Boles, M.A. Thermodynamics; McGraw-Hill: New York, 1994.

Exergy, a Convenient Concept 71

7Chemical Exergy

In the last chapter the concepts of exergy and physical exergy, in particular,were introduced. This chapter deals with three other important concepts—namely, exergy of mixing, chemical exergy, and cumulative exergy con-sumption—and their numerical evaluation.

1 INTRODUCTION

Recall that exergy values reflect to which extent a compound or mixture isout of equilibrium with our environment. Examples are differences inpressure and temperature with the environment. Differences in temperaturelead to heat transfer, while differences in pressure lead to mass flow. Chapter6 shows that the physical exergy represents the maximum amount of workthat can be obtained from a system by converting a system’s pressure andtemperature to those of our environment.

It appears, however, that when a system’s physical exergy is zero andthus the system prevails in a state of thermomechanical equilibrium with theenvironment, it may still be out of equilibrium with that environment inother respects. The origin is to be found in the difference in the compositionand nature of the components making up the system and the environment,respectively. These differences lead to values for the exergy of mixing and thechemical exergy. Earlier we pointed out that though the physical exergy ofmethane is zero, its chemical exergy is not. Equally, pure nitrogen andoxygen have nonzero chemical exergies because their mole fraction in theenvironment is different from 1. Because the process of mixing plays an im-portant role in the determination of the chemical exergy, the next sectiondeals with the exergy of mixing.

73

2 EXERGY OF MIXING

To clarify the concept of the exergy of mixing, we give the example of pureoxygen at ambient conditions P0 and T0. Consider a system, for conveniencechosen at P0, T0, isolated from the environment and consisting of twoseparate compartments containing oxygen and air, respectively. The twocompartments, initially separated by an elastic diathermal barrier, and thusin mechanical and thermal equilibrium, are brought in contact with eachother by removing the barrier. Oxygen and air will diffuse into each other,and eventually an equilibrium will be reached where oxygen and air havemixed into a homogeneous mixture. The initial condition of oxygen isapparently not one of complete equilibrium with the environment (i.e., withair) despite the equality in pressure (P0) and temperature (T0). Thethermodynamic potential of pure oxygen is higher than that of oxygen inair at P0 and T0. On mixing of the components of air in their pure state to ahomogeneous mixture, the thermodynamic potential of each componentdecreases. The associated change in exergy is

DmixEx ¼ DmixH� T0DminS ð1ÞAs the mixing process takes place at P0, T0, we may write

DmixExP0T0¼ DmixGP0T0

ð2ÞFor the calculation of the exergy value at P, T of a mixture, of a given

composition, with respect to the exergy values of the pure components at Pand T, the exergy difference is defined as

ExmixuDmixEx ð3Þwith values for DmixH and DmixS at the conditions P and T. Chapter 10presents an example of the industrial distillative separation of the mixture ofpropane and propene, in which the exergy of mixing is very prominent.

3 CHEMICAL EXERGY

For the determination of a compound’s chemical exergy value we need todefine a reference environment. This reference environment is a reflection ofour natural environment, the earth, and consists of components of the at-mosphere, the oceans, and the earth’s crust. If, at P0 and T0, the substancespresent in the atmosphere, the oceans, and the upper part of the crust of ourearth are allowed to react with each other to the most stable state, the Gibbs

Chapter 774

energy of this whole system will have decreased to a minimum value. Wethen can define the value of the Gibbs energy for a subsystem, the ‘‘referenceenvironment’’—at sea level, at rest, and without other force fields presentthan the gravity field—to be zero as well as for each of the phases presentunder these conditions. It is a logical extension of these assumptions todefine the thermodynamic potentials of each of the substances present in thedifferent phases to have a value of 0 J/mol. With respect to this ‘‘referenceenvironment,’’ we then determine the thermodynamic potentials of all kindsof substances in all kinds of phases at P and T. From this ‘‘referenceenvironment’’ it is not possible to obtain any work. Therefore, this state isalso meaningful as a reference state for the determination of exergy values atP0 and T0. This finally leads to the definition Exi (P0, T0) u Ai (P0, T0) forthe subsystem at sea level, at rest, and without the presence of any otherforce field than the gravity field. The concept of this ‘‘reference environ-ment’’ is illustrated for a number of the so-called reference components.

3.1 Reference Components from Air

Apart from differences in chemical concentration, or better, thermodynamicpotentials, such as for oxygen, there can be other situations for being out ofequilibrium with the environment at P0, T0. Consider, for instance, thematerial graphite. Graphite can spontaneously react with oxygen to fromcarbon dioxide, but for kinetic reasons the reaction is very slow and graph-ite seems to be stable in our environment, although in the presence of oxy-gen it is metastable with respect to carbon dioxyde. As a result, it has asignificant amount of chemical exergy available and can be considered as animportant energy carrier because it is highly out of equilibrium with theenvironment.

In our environment there are many substances that, like oxygen in ouratmosphere, cannot further diffuse and/or react toward more stable config-urations and may be considered to be in equilibrium with the environment.Neither chemical nor nuclear reactions can transform these components intoeven more stable compounds. From these components we cannot extractany useful work, and therefore an exergy value of 0 kJ/mole has beenassigned to them. This has been done for the usual constituents of air: N2,O2, CO2, H2O, D2O, Ar, He, Ne, Kr, and Xe at T0 = 298.15 K and P0 =99.31 kPa, the average atmospheric pressure [1]. Their partial pressures Pi inair are given in Table 1.

From these data we can calculate the, chemical, exergy values of thesecomponents in the pure state at P0 and T0. Air at these conditions can, to agood approximation, be considered as an ideal gas, therefore, separationinto its constituents will take place without a heat effect: DsepH = 0. And so

Chemical Exergy 75

the only effect left in the exergy change of separation, DsepEx = � Exmix [seeEq. (3)], is that of the entropy of separation:

DsepEx ¼ DsepH� T0DsepS ð4Þ¼ T0DmixS

As we recall from Chapter 2, the change in entropy associated with takingone mole of an ideal gas isothermally from pressure P1 to a pressure P2 isgiven by

DS ¼ �Rln P2

P1

� �ð5Þ

From this equation we can show [2] that the standard chemical exergy at P0

and T0 of a pure component can be calculated from its partial pressure Pi inair with Eq. (6):

Ex0ch;i ¼ RT0lnP0

Pi

� �ð6Þ

The standard chemical exergy values for the main constituents of air aslisted in Table 1 are given in Table 2.

Table 1 Partial Pressure of Various Components in Air

Component Pi (kPa) Component Pi (kPa)

N2 75.78 He 0.000485

O2 20.39 Ne 0.00177CO2 0.0335 Ar 0.906H2O 2.2 Kr 0.000097

D2O 0.000342 Xe 0.0000087

Table 2 Standard Chemical Exergy Values at P0,T0 of VariousComponents Present in Air

Component Exch0 (kJ/mol) Component Exch

0 (kJ/mol)

N2 0.72 He 30.37O2 3.97 Ne 27.19

CO2 19.87 Ar 11.69H2O 9.49 Kr 34.36D2O 31.23 Xe 40.33

Chapter 776

Exergy values for the elements in their stable modification at T0 =298.15 K and P0 = 101.325 kPa are called standard chemical exergy valuesExch

0 . For the calculation of the chemical exergy value of all kinds ofsubstances, the standard chemical exergy values of all elements are required.

3.2 Exergy Values of the Elements

The following example for graphite illustrates how the chemical exergyvalue for all other elements can now be calculated (Table 3). For thecalculation of Exch

0 of graphite, we make use of the reaction in which CO2

is formed from the elements in their stable modification at P0, T0:

Cðgraphite; sÞ þO2ðgÞ ! CO2ðgÞ ð7Þ

Table 3 Standard Chemical Exergy Values of the Elements [1]

Element Ex0ch (kJ/mol) Element Ex0ch (kJ/mol)

Ag (s) 70.2 Kr (g) 34.36

Al (s) 888.4 Li (s) 393.0Ar (g) 11.69 Mg (s) 633.8As (s) 494.6 Mn (sa) 482.3

Au (s) 15.4 Mo (s) 730.3B (s) 628.5 N2 (g) 0.72Ba (s) 747.7 Na (s) 336.6Bi (s) 274.5 Ne (g) 27.19

Br2 (1) 101.2 Ni (s) 232.7C (s, graphite) 410.26 O2 (g) 3.97Ca (s) 712.4 P (s, red) 863.6

Cd (sa) 293.2 Pb (s) 232.8Cl2 (g) 123.6 Rb (s) 388.6Co (sa) 265.0 S (s, rhombic) 609.6

Cr (s) 544.3 Sb (s) 435.8Cs (s) 404.4 Se (s, black) 346.5Cu (s) 134.2 Si (s) 854.6D2 (g) 263.8 Sn (s, white) 544.8

F2 (g) 466.3 Sn (s) 730.2Fe (sa) 376.4 Ti (s) 906.9H2 (g) 236.1 U (s) 1190.7

He (g) 30.37 V (s) 721.1Hg (1) 115.9 W (s) 827.5I2 (s) 174.7 Xe (g) 40.33

K (s) 366.6 Zn (s) 339.2

Chemical Exergy 77

The corresponding change in standard Gibbs energy is called thestandard Gibbs energy of formation of CO2, Df G

0298.15, and is defined as

DfG0298:15u

XriA0i;298:15 ð8Þ

in which ri is the so-called stoichiometric coefficient, defined as positive forproducts and negative for reactants, and Ai0 = Gi

0 is the standard thermo-dynamic potential or Gibbs energy for substance i. Equation (8) is based onthe formation of 1 mole of the compound considered, in this instance 1 moleof CO2. If we define the change in exergy in the same way:

DfEx0298:15 ¼ Df G

0298:15 ¼

Xi

riA0i;298:15ð9Þ

uX

riEx0ch;i

then the exergy of graphite can be calculated from

Ex0ch;CðsÞ ¼ �Df G0298:15 þ 1 � Ex0ch;CO2ðgÞ � 1 � Ex0ch;O2ðgÞ ð10Þ

The values of Df G298.150 for many compounds are listed in standard tables

[2], and the value for CO2 reads �394.359 kJ/mole. With the help of Table 2,which gives the standard chemical exergy values for CO2 and O2, Equation(10) allows the calculation of Exch,C(s)

0 = 394.359 + 19.87 � 3.97 = 410.26kJ/mole.

For the remaining elements, reference compounds have been chosen,as they occur in seawater or in the lithosphere, the earth’s crust. Animportant aspect of this choice has been that the calculated exergy valuesof most compounds should be positive. Table 3 lists the standard chemicalexergy values of the elements as presented in Szargut’s well-known standardwork [1]. Chapter 8 gives an example, the adiabatic combustion of H2, toillustrate the use of these exergy values in an interesting application.

3.3 Chemical Exergy Values of Compounds

Table 3 is useful for the calculation of the standard chemical exergy valuesof compounds. We illustrate this for methane and start from its hypotheticalformation reaction at standard conditions:

CðsÞ þ 2H2ðgÞ ! CH4ðgÞ ð11ÞApplying Eq. (9) results in

Ex0ch;CH4ðgÞ ¼ Df G0298:15 þ Ex0ch;CðsÞ þ 2Ex0ch;H2ðgÞ ð12Þ

The first term on the right-hand side of this equation is the standard Gibbsenergy of formation of methane, which is listed [2] as �50.460 kJ/mole and

Chapter 778

thus Ex0ch,CH4(g)can be calculated to be 831.6 kJ/mole. Chapter 9 illus-

trates the use of this exergy value in the analysis of a natural gas-drivenpowerstation.

In general, we can calculate the standard chemical exergy of a com-ponent j from the standard chemical exergy of its elements with the equation

Ex0ch; j ¼ DfG0j;298:15 þ

XviEx

0ch;i ð13Þ

We recall that the exergy of methane will be different for other valuesof P and T than P0, T0 and refer to Table 1 of Chapter 6 to demonstrate theinfluence of pressure and temperature on this exergy value. It is clear thatthe chemical contribution to the total exergy, Ex = Exphys + Ex0ch, in thiscase is dominant. At the same time we should be aware that in a simplecompression step this contribution is irrelevant and should not be includedin an exergy efficiency calculation. On the level of, let us say, 10 kJ/mole ofphysical exergy, the loss of 2.5 kJ/mole of exergy due to inefficiencies of thecompressor results in a thermodynamic or exergetic efficiency of 75%. Hadwe included the 832 kJ of chemical exergy of methane, the thermodynamicefficiency would have been as high as 99.7%, which gives a completelyblurred picture of the compressor’s performance.

Finally, Table 4 gives the standard exergy values of a selected numberof compounds that are relevant for the examples and topics presented in thisbook.

Table 4 Standard Chemical Exergy Values ofSelected Compounds

Substance kJ/mole

CH4 (g) ‘‘natural gas’’ 832CH3OH (g) 722

CH3OH (l) 718UCH2U

a ‘‘oil’’ 652(CH2O)b ‘‘biomass’’ 480

CO2 (g) 20SiO2 (s, a quartz) 1.9TiO2 (s, rutile) 21.4Al2O3.H2O (s) ‘‘bauxite’’ 200.8

Fe2O3 (s) ‘‘haematite’’ 16.5NH3 (g) 337.9CO(NH2)2 (s) urea 689.0

a Crude oil on a per-carbon basis.b Biomass (glucose) on a per-carbon basis.

Chemical Exergy 79

3.4 The Convenience of the Chemical Exergy Concept

In chemical thermodynamics the reference components have been selectedas the elements in their most common state at standard conditions, thestandard state. These elements have been defined as having a zero standardGibbs energy of formation. The standard Gibbs energy of formation of acompound is related to that of the elements from which it has beencomposed. Let us take liquid methanol, CH3OH [1]. Its standard Gibbsenergy of formation is �166.270 kJ/mole, a number that does not say verymuch other than that in the reaction

CðsÞ þ 2H2ðgÞ þ 1

2O2ðgÞ ! CH3OHð1Þ ð14Þ

the standard Gibbs energies at the left-hand side are zero and the standardGibbs energy of reaction is also �166.270 kJ/mole. However, following theprocedures as outlined in the above sections, we can calculate with Eq. (13)the standard chemical exergy of liquid methanol to be �166.270 + 410.26 +2 � 236.10 + 1/2 � 3.97 = 718.2 kJ/mole. This number is very meaningful,as it expresses the maximum amount of work available to us embodied in onemole of liquid methanol. We can then compare this with the value formethane and notice that the partial oxidation of methane to methanol haslowered the exergy value somewhat, from 832 kJ/mole to 718 kJ/mole. Butmethanol is in the liquid state, and this is an attractive feature for atransportation fuel. On the other hand, methanol has double the mass ofmethane, and so per unit of mass its available work or exergy is less than half.And last but not least, the efficiency of converting methane into methanolmay be about 50–60% (see Chapter 14) and much of the advantage of usingmethanol seems to have gone. Nevertheless, although, strictly speaking, theconcept of exergy does not add anything in the fundamental sense, itcertainly adds convenience—for example, for the discussion on the prosand cons of energy conversion such as in the above comparison of methaneand methanol. This is one of the attractive features of the exergy concept thathas made it so popular with many practitioners.

4 CUMULATIVE EXERGY CONSUMPTION

Suppose we deal with a process in which iron, Fe, has to be used as areactant, for example in a reduction reaction. The standard chemical exergyof Fe is 376.4 kJ/mole. If we wish to carry out a thermodynamic or exergyanalysis of this process, this value is not appropriate. After all, to put theexergy cost of the product, for which Fe was needed as a reactant, in proper

Chapter 780

perspective, we need to consider all the exergetic costs incurred in order toproduce this product all the way from the original natural resources—ironore and fossil fuel in this example. The production of iron from, for ex-ample, the iron ore haematite and coal has a thermodynamic efficiency ofabout 30% [1], and therefore it is not 376.4 kJ/mole Fe that we need toconsider but 376.4/0.3 = 1250 kJ/mole Fe. This value is called the cumu-lative exergy consumption (CExC) of Fe. It may well be that for properanalysis of the efficiency of the step consuming Fe to produce the product,we want to take the standard chemical exergy of Fe, but for the calculationof the CExC of the final product, we need to include the CExC of Fe.Chapter 14 discusses many examples where the exergy of the final product iscompared with the CExC of the same product. Together these two valuesallow the calculation of the thermodynamic, exergetic, efficiency of a processyielding the product from natural resources. This is part of the subject ofChapter 14.

We recall that, without mentioning it, we touched upon the topic ofcumulative exergy consumption before. In Chapter 6 we illustrate theapplication of the concept of physical exergy with the simple example ofmixing liquid water of 100jC with that of 0jC. In that example we first takethe exergy value of hot water as 34 kJ/kg. But when this water has beenproduced from natural gas, its accumulated exergy consumption is calcu-lated according to Table 2 of Chapter 6 to be 1/0.12 � 34 = 283 kJ/kg.

Finally, we consider another important contributor to the CExC of aproduct. We refer to the equipment being used in the process. This equip-ment also has to be manufactured from resources originally taken from theenvironment. This cumulative exergy consumption has to be discountedover the lifetime of this equipment and then added as a contribution to thecumulative exergy consumption of the product. Our experience is that thiscontribution is negligible for equipment that works continuously. For equip-ment performing with an irregular operation such as a laundry machine athome, this contribution may be substantial and makes up a large part of thetotal exergy cost of the product.

5 CONCLUSIONS

The concept of chemical exergy has a distinct advantage over the standardGibbs energy of formation. Whereas the latter is zero for the elements atstandard conditions, the chemical exergy has a zero value for compounds orelements in equilibrium with and as they occur in our natural environment.Thus the standard chemical exergy of a compound clearly represents theamount of work available with respect to the environment in which we live

Chemical Exergy 81

and work. The chemical exergy can be simply calculated from the Gibbsenergy of formation. The only difference between the two concepts is thattheir zero values are defined for different reference substances.

The chemical exergy of a molecule in a mixture is smaller than in itspure state, as it will require work to separate the mixture in its pureconstituents, the exergy of separation. This exergy will be lost as the exergyof mixing when the pure constituents spontaneously form the mixture. Thetotal exergy of a pure compound or element is therefore composed of threecontributions: the chemical exergy; the exergy of mixing, and the physicalexergy. The last element accounts for the fact that the molecule may be atdifferent conditions of pressure and temperature than those of the environ-ment, P0 and T0.

The concept of cumulative chemical exergy consumption is very usefuland accounts for the fact that when a compound (e.g., ammonia) isintroduced into a process, its chemical exergy has to be corrected for theexergy consumption accumulated since this compound was manufacturedfrom its natural constituents (air and natural gas in the case of ammonia).

If the thermodynamic efficiency of a process step is calculated, thechemical exergies should be excluded from the calculation if the process stepdoes not include chemical conversions. If it does, it may be appropriate todistinguish between the physical and the chemical efficiency, Dphys and Dchem,of the process step.

Finally, although the exergy concept is not strictly necessary for thecalculation of the available work lost in the process, it is an extremely handytool to calculate losses and efficiencies and for making a quick assessment ofprocess options. Chapter 8 gives some simple illustrations, whereas Part III,Case Studies, presents the results of integrated studies in the world of energyand chemical technology.

REFERENCES

1. Szargut, J.; Morris, D.R.; Steward, F.R. Exergy Analysis of Thermal, Chemical,

and Metallurgical Process; Hemisphere Publishing Corp.: New York, 1988.2. Smith, J.M.; Van Ness, H.C.; Abbott, M.M. Introduction to Chemical Engi-

neering Thermodynamics, 5th ed.; McGraw-Hill: New York, 1996.

Chapter 782

8Simple Applications

In this chapter we present some examples of simple applications of exergyanalysis. All applications refer to process steps such as the spontaneousexpansion of a gas, the production of ice from water by cooling withevaporating ammonia in a heat exchanger, the compression of a gas, thevortex tube, the separation of a mixture, and the spontaneous combustion ofhydrogen. Chapters 9 to 11 in Part III, Case Studies, deal with the analysis ofcomplete processes, which consist of a sequence of process steps.

1 PROBLEM 8.1

The conditons of a natural gas reservoir are 30 MPa and 100jC. The gas,assumed to be pure methane, is spontaneously expanded to a pressure of 7MPa (Fig. 1). Assuming that this expansion is adiabatic, calculate theamount of work that is lost in the process, and express it as a fraction ofthe originally available amount of work per mole of gas in the reservoir.Carry out this calculation while making a distinction between the physicaland chemical exergy of the gas.

Assume t0=20.00jC.

2 SOLUTION TO PROBLEM 8.1

The expansion of the natural gas is a spontaneous process and thus workmust have been lost. According to the Gouy–Stodola relation, this lost workis related to the entropy production of the process.

Wlost ¼ T0Sgen ð8:1Þ

The expansion has been assumed to be adiabatic, and thus the entropygenerated equals the entropy increase of the gas, DS, as the entropy change

83

of the environment, DS0, can be set to zero because the process is adiabatic.The amount of lost work can now be calculated from the entropy values S1

and S2 of one mole of methane at the initial and final conditions, re-spectively. However, this requires knowledge not only of the final pressureP2, which is known, but also of the final temperature T2, which is unknown.Here the first law helps us out. Applying Eq. (2.39) and substituting zero forWin and Qout, we find DH = 0 or H2 = H1. From the IUPAC data seriesnumber 16, dealing with methane [1], we find that the molar enthalpy andentropy at initial conditions are respectively 501.9 J/mol and �44.22 J/molK. Thus H2 has the same value of 501.9 J/mol, but now at P2 = 7 MPa andthe unknown value of T2. This allows us to find T2 = 336.13 K and at thesame time S2 = �32.88 J/mol K from the same reference.

Thus the lost work can be calculated and we find Wlost = T0 (S2�S1)= 3324 J/mol. Note that this calculation did not require the application ofthe concept of exergy.

Next we wish to calculate which fraction this lost work is of the workoriginally available in the gas. The chemical exergy of the gas, assumed to bemethane, is significant, 831.65 kJ/mol, but it should be excluded from thecalculation because no chemistry is involved in the expansion step. Thework available in the gas at initial and final conditions can be calculatedfrom Eq. (6.11):

Ex ¼ ðH�H0Þ � T0ðS� S0Þ ð6:11Þ

From [1] we can find the values for H1, S1, H2, S2, and H0, S0. They are501.9 J/mol, �44.22 J/mol K, 501.9 J/mol, �32.88 J/mol K, and �194 J/moland �0.54 J/mol K, respectively. These last two values relate to the stablestate of methane at P0 = 0.1000 MPa and T0 = 293.15 K, which is the gas

Figure 1 The adiabatic expansion of ‘‘natural gas.’’

Chapter 884

phase. We calculate Ex1 = 13.501 and Ex2 = 10.176 kJ/mol. Of course, weshould find the same amount of lost work as before, 3.325 kJ/mol, from

Wlost ¼ Ex1 � Ex2 ð8:2ÞThe fraction of nonchemical work available in the gas that has been lost inthe expansion process can now be calculated from Wlost/Ex1 = 3.325/13.501= 0.246. If we had included the chemical exergy of the gas, this numberwould have been reduced to 0.00393, but as the expansion step is strictlynonchemical, this result is meaningless. Of course, the calculation of Wlost

itself would not be affected as the chemical exergy would have to be includedin both Ex1 and Ex2 and would drop out.

3 PROBLEM 8.2

Water at 20jC is cooled and frozen to ice at 0jC in a countercurrent processwith evaporating ammonia (see Fig. 2). The minimum temperature differ-ence required for proper heat transfer is taken as 5jC between solid ice andliquid NH3 (Fig. 3). Heat exchange takes place in equipment well isolatedfrom the environment. Calculate

1. The exergy of 1 mole of ice2. The mass flow rate of ammonia for the production of 1 mole/sec

of ice3. The amount of work lost in this process step4. The efficiency of this process step

4 SOLUTION TO PROBLEM 8.2

1. We assume t0 = 20jC. Next we use the steam tables [2] to find thevalues for H0

1, S01 at 20jC in state 1 and at 0jC in state 2 for liquid water, H2

1

and S21. These are 1511 J/mol, 5.339 J/mol K, �0.7 J/mol, and 0 J/mol K,

Figure 2 Freezing of water with the help of evaporating liquid ammonia.

Simple Applications 85

respectively. From the heat and temperature of fusion, DfusH = 6008 J/moland Tfus = 273.15 K, we can calculate the enthalpy and entropy at 0jCaccording to

Hs2 ¼ Hl

2 � DfusH

Hs2 ¼ �0:7� 6008 ¼ �6008:7 J=mol

and

Ss2 ¼ S1

2 � DfusH=Tfus

Ss2 ¼ 0� 6008

273:16¼ �21:99 J=mol K

Then we apply Eq. (6.11) to calculate the exergy of 1 mole of ice

Exs2 ¼ ðHs2 �Hl

0Þ � T0ðSs2 � Sl

0Þand find Ex2

s = 491.8 J/mol, which is the exergy of 1 mole of ice at 0jC.2. Next we turn our attention to ammonia. What are the conditions

of the evaporating ammonia? As the minimum temperature differencebetween ammonia and water is 5jC, t4 = t3=�5jC (Fig. 3). State 3 issaturated ammonia in the liquid state, and state 4 is saturated ammonia inthe vapor state. At this temperature the saturated vapor pressure ofammonia is PNH3

sat = 0.2951 MPa. From the data compilation by Vargaftiket al. [3] we find for these conditions H4

v = 28.103 and H3l = 6.020 kJ/mol.

The heat exchanger operates adiabatically with respect to the environment;neither heat nor work is exchanged with the environment, thus the overallenthalpy change must be 0 according to the first law, Eq. (2.39). Therefore,

n:NH3ðHv

4 �H l3Þ ¼ n

:H2OðH l

1 �H s2Þ ð8:3Þ

As _nH2O= 1 mol/s, we can calculate for _nNH3

= 0.3405 mol/s.

Figure 3 Temperature profiles in the heat exchange of Fig. 2.

Chapter 886

3. The amount of lost work, Wlost, can again be calculated from theGouy–Stodola equation, Eq. (3.12). This requires the values for Sl

1 = S0l

and S2s for water and S3

l and S4v for ammonia. These last values can again be

found from Vargaftik et al. [3] and are 65.17 and 149.13 J/mol K,respectively. First we calculate _Sgen from _Sgen = _nH2O

(S s2 � S l

1)+ _nNH3

(Sv4 � S l

3) = 1.260 J/Ks. Application of the Gouy–Stodola relation gives_Wlost = 0.369 kW/(mol ice).

We could also have calculated _Wlost by making use of the equation

W:lost ¼ E

:xin � E

:xout ð8:4Þ

with _Exin = _nH2OExl1 + _nNH3

Exl3 and_Exout = _nH2O

Exs2 + _nNH3Exv4. All en-

thalpy and entropy values are available to perform this calculation. Exl1 =(H0 � H0)�T0(S0 � S0)=0 J/mol, Exl3 = 6,020 – 29,481 � 293.15 (65.17 �162.74) = 5141 J/mol, Ex2

s = 491.8 J/mol, and Ex4v = 28,103 � 29,481 �

293.15 (149.13 � 162.74) = 2612 J/mol. We then can calculate _Exin and_Exout . These values are _Exin = 1�0 + 0.3405 � 5141 = 1750 W, _Exout =1�491.8 + 0.3405� 2612 = 1381W. Applying Eq. (8.4), we again find _Wlost =0.369 kW/(mol/ice).

4. To calculate the efficiency of this process step, we can compare_Exout and _Exin. Defining the efficiency D as

DuE:xout

E:xin¼ 1381

1750ð8:5Þ

we find D = 0.789. Although the exchange of heat has taken place with anefficiency of 100%, the equipment is ‘‘well-isolated,’’ the exchange of exergyhas necessarily asked a sacrifice in exergy due to the required temperaturedifferences between the two flows, which change from 20�(�5) = 25jC atthe entrance point to 5jC at the point of exit of ice.

A more reasonable definition of the efficiency is, however, the com-parison of the exergy change of the water and the exergy transferred fromthe working medium, in our case ammonia. This efficiency is defined as

DuExs2 � Exl1Exl3 � Exv4

¼ 491:8

0:3405ð5141� 2612Þ ð8:6Þ

We now find D = 0.571.

5 PROBLEM 8.3

A manufacturer of compressors wants to determine the efficiency of thispiece of equipment. In one experiment the compression of one mole of gas

Simple Applications 87

per second from P1 = 5 bar to P2 = 20 bar requires a power input of _Win =5.271 kW. During this experiment the temperature of the gas rises from t1 =t0 = 20jC to t2 = 160.0jC. What is the efficiency of the compressoraccording to the definition

DuW:

revin

W:in

ð8:7Þ

The gas may be assumed to behave as an ideal gas, its cp value may beconsidered at a constant value of 37.65 J/molK and the gas constant R =8.314 J/mol K. The compressor may be assumed to operate adiabatically.

6 SOLUTION TO PROBLEM 8.3

The first law applied to this problem reads

Win ¼ DHþQout ð8:8Þand as the compressor operates adiabatically Qout = 0 J, so

Win ¼ DH ð8:9ÞThe gas may be assumed to behave as an ideal gas, and its enthalpy istherefore only a function of temperature, not of pressure:

DH ¼ cpðT2 � T1Þ ð8:10Þ¼ 5271 J=mol

The second law reads

Sgen ¼ DSþ DS0 ð8:11ÞAs the compressor operates adiabatically, the entropy change of theenvironment, DS0=0 J/K. The change in entropy of one mole of the idealgas can be calculated from Eq. (2.43).

DS ¼ cp ln T2=T1 � R ln P2=P1 ð8:12Þand is found to be 3.173 J/mol K. According to Eq. (8.11), this value is alsothe value for the generated entropy Sgen. The minimum amount of workis required when the process is carried out reversibly; this is in the limit as thedriving forces are going to zero and thus with DS= Sgenerated = 0 J/K. FromEq. (8.12) it follows elegantly that T2

rev < T2. This equation allows thecalculation of T2

rev = 125.0jC by putting DS=0 and shows clearly that T2rev

is indeed the minimum value for T2. The more T2 exceeds T2rev, the higher DS,

Sgen, and Wlost and the lower the efficiency of the compressor will be. This

Chapter 888

also follows from combining Eqs. (8.7) and (8.9) for both T2rev andT2 actually

measured,

DauW rev

in

Win¼ cpðT rev

2 � T1ÞcpðT2 � T1Þ ¼

Win �Wlost

Winð8:13Þ

We find Da = 0.750.The work lost in the process is Wlost = T0Sgen and is calculated to be

930 J/mol. If the thermodynamic efficiency is calculated from

DbuExoutExin

¼ Ex2Ex1 þWin

¼ Ex2Ex2 þWlost

ð8:14Þ

we find Db = 0.899. In Eq. (8.14) we use that Wlost = Exin � Exout with Exin= Ex1 + Win and Exout = Ex2. The latter value has been calculated fromEx2 = (H2�H0)� T0(S2� S0) = cp(T2�T0)� T0 cp ln T2/T0�R ln P2/P0=8263 J/mol.

The efficiency Da calculated with Eq. (8.13), and the one calculatedwith Eq. 8.14, Db, are different, which can be seen from the followingalternative expressions:

Da ¼ Win �Wlost

Winð8:15Þ

and

Db ¼ Ex1 þWin �Wlost

Ex1 þWinð8:16Þ

The second efficiency, Db, also accounts for the exergy of the entering flow,whereas the first efficiency, Da, does not. Wlost is the same in both cal-culations. There is much to say for considering Da as the value that expressesthe performance of the compressor best. Da expresses in a meaningful waythe performance of the equipment whereas Db expresses the quality of theprocess.

7 PROBLEM 8.4

A stream of gas of ambient temperature t1 = t0 = 20jC and at a pressure ofP1 = 0.8 MPa is claimed to be separated adiabatically (Fig. 3) into twoequal flows of t2 = 70jC and t3 = �30jC, respectively, both at P2 = P3 =0.1 MPa. The gas may be assumed to behave as an ideal gas with a constantcp value of 30 J/mol K.

1. Show that this process is possible.2. Determine the exergetic efficiency of the process.

Simple Applications 89

8 SOLUTION TO PROBLEM 8.4

1. Whenever the question of ‘‘being possible’’ crops up, the secondlaw offers relief. The first law shows that the overall enthalpy of the processdoes not change as no work is performed and no heat is exchanged with theenvironment. Based on 1 mole of gas splitting in two streams of 1/2 moleeach, we can write

DH ¼ 1

2ðH2 �H1Þ þ 1

2ðH3 �H1Þ ¼ 0 ð8:17Þ

Equation (8.17) can be simplified in the case of ideal gases (with constant Cp

values) to

1

2cpðT2 � T1Þ þ 1

2cpðT3 � T1Þ ¼ 0

or can be written as

ðt2 � t1Þ þ ðt3 � t1Þ ¼ 0

the relation of which is satisfied indeed.The second law according to Eq. (8.11) simplifies to the equation

DS = Sgen > 0. The process is possible if the overall change in entropy ofthe streams is positive and indeed it is, as follows from applying Eq. (8.12).

DS ¼ 1

2cp ln

T2

T1þ 1

2cp ln

T3

T1� R ln

P2

P1 ð8:18Þ¼ 2:36� 2:81þ 17:29 ¼ 16:84 J=K

It is obvious from comparing the third term at the right side of theequation with the other two terms that it is the pressure difference betweenthe initial and final states that more than compensates for the separation of

Figure 4 Adiabatic splitting of a compressed gas into two flows of differenttemperatures.

Chapter 890

the original stream at temperature T0 in a stream at a higher and one at alower temperature, a phenomenon that intuitively feels as ‘‘unlikely’’ andindeed is associated with a decrease in entropy as reflected by the two firstterms right of the equal sign.

2. To explain the possibility of the process of splitting the originalstream into one of a higher and one of a lower temperature, an exergy analysisis very revealing. If we assume that kinetic and potential energy contributionsto the exergy values of the streams can be neglected, the exergy of the originalstream is

Ex1 ¼ ðH1 �H0Þ � T0ðS1 � S0Þ ð6:11Þ

Ex1 ¼ cpðT1 � T0Þ � T0ðcp ln T1

T0� R ln

P1

P0Þ ð8:19Þ

and as T1 = T0 = 293.15 K, P1 = 0.8MPa, and P0 = 0.1MPa, Ex1 becomesRT0 ln 8 = 5068 J.

The exergy of the split streams is

Ex2 ¼ 1

2cpðT2 � T0Þ � T0ðcp ln T2

T0� R0 ln

P2

P0Þ

� �ð8:20Þ

which gives Ex2 = 57.5 Jand

Ex3 ¼ 1

2cpðT3 � T0Þ � T0ðcp ln T3

T0� R0 ln

P3

P0Þ

� �ð8:21Þ

resulting in Ex3 = 72.3 J.From comparing Ex1 = 5068 J with Ex2 + Ex3 = 130 J, it is clear that

the work available in the original single stream is more than enough toaccount for the work available in the split streams together, and we find anefficiency for our case of D = (Ex2 + Ex3)/Ex1 = 3% and 97% is lost.Originally, this piece of equipment was described by Hilsch [4] and Ranque[5] and was named after them the Hilsch–Ranque tube or the Vortex tube.In fact, a much larger separation in temperature T2 and T3 should bepossible, as Ex1 is considerably larger than Ex2 + Ex3. This is in line withthe claimed efficiency of the modern version of the tube, the ‘‘Twister’’ tube,as this piece of equipment is now called [6]. The ‘‘Twister’’ tube is used topartially condense higher hydrocarbons from natural gas to bring the gas onspecification such that condensation in the transport system is avoided.

Simple Applications 91

9 PROBLEM 8.5

Air, assumed to be a mixture of 79 mole % nitrogen (N2) and 21 mole %oxygen (O2), is split into its pure components also at ambient conditions P0,T0 with P0 = 1 bar and T0 = 293.15 K (Fig. 5). Under these conditions airbehaves as an ideal gas.

Calculate the minimum amount of work required for the separation ofone mole of air.

10 SOLUTION TO PROBLEM 8.5

The exergy of separation, Exsep, is given by

Exsep ¼ 0:79ExoN2þ 0:21ExoO2

� 1 � Exoair ð8:22Þ

ExN2

o and ExO2

o are the chemical exergy values of the pure components ofair. The exergy value of air at standard conditions is given by

Exoair ¼ 0:79ExoN2þ 0:21ExoO2

þDmixH� T0DmixS ð8:23Þ

For 1 mol of an ideal gas mixture, DmixH = 0 J/mol and DmixS =�R S xiln xi, where xi is the mole fraction of component i in the mixture. For air:xN2

= 0.79 and xO2= 0.21. The exergy values of the pure components of air

cancel against each other so Exsep can be simplified to Exsep = �RT0 S xiln xi. Substitution of the given mole fractions of T0 and the gas constant Rthen give Exsep = 1253 J/mol.

This is the minimum amount of work required. In practice, the workrequirement is much larger due to the inefficiencies of the real separationprocess. This is clearly illustrated in Chapter 10 for the separation bydistillation of a mixture of propane and propene.

Figure 5 The separation of air into its main components.

Chapter 892

11 PROBLEM 8.6

Pure hydrogen gas at room pressure and temperature is adiabaticallycombusted with air. The combustion takes place with an amount of airthat is 30% in excess of what is stoichiometrically required. Calculate theadiabatic flame temperature of the process, the work lost, and the thermo-dynamic efficiency of the process. Assume air to consist of a mixture of 79mol % of N2 and 21 mol % of O2.

12 SOLUTION TO PROBLEM 8.6

The equation for the stoichiometric combustion of hydrogen is

H2ðgÞ þ 1

2O2ðgÞ ! H2OðgÞ ð8:24Þ

With 30% excess air, Eq. (8.24) reads

H2ðgÞ þ 0:65O2ðgÞ þ 2:445N2ðgÞ�!H2OðgÞ þ 0:15O2ðgÞþ 2:445N2ðgÞ

ð8:25Þ

Assume that the hydrogen feed stream is 1 mol/s. The reactants are fedto the combustor at 298.15 K and 0.1 MPa, and the heat of reaction will beused to raise the temperature of the product mixture to its final value, theadiabatic flame temperature. The first law for this adiabatic process can bewritten as

DH:¼ 0 ¼

DrH:0298:15K þ n

:H2O

Z T

298:15K

CP;H2OdTþ n:O2

Z T

298:15K

CP;O2dTþ n

:N2

Z T

298:15K

CP,N2dT

!

ð8:26Þwith n

:H2O

= 1.0, n:O2

= 0.15, n:N2

= 2.445 mol/s, and T is the final exittemperature of the products. We make the additional assumption that thegas is ideal. This allows us to use the ideal gas molar heat capacity values atconstant pressure. The following expression for the temperature dependencyof the heat capacity Cp

ig is used:

CigP

R¼ Aþ BTþ D

T 2ð8:27Þ

where the coefficients A, B, and D are given in Table 1.The reaction enthalpy is �241,818 J/mol H2 and is obtained from

standard tables [2]. Substitution of this and Eq. (8.27) into Eq. (8.26) yields

0 ¼ �241;818þ 8:314

Z T

298:15K

Xi

_niAi þXi

_niBiTþXi

_niDi

T 2

!dT ð8:28Þ

Simple Applications 93

From Table 1, we can readily compute Si _niAi ¼ 12:035 � s�1; Si _niBi ¼2:976� 10�3K�1 � s�1, andSi _niDi ¼ 0:1848� 105K2 � s�1. Substitution yields

0 ¼ �241;818þ 8:314

�12:035ðT� 298:15Þ þ 1=2 2:976

� 10�3ðT 2 � 298:152Þ � 0:1848� 1051

T� 1

298:15

� �� ð8:29Þ

Solution of this algebraic equation yields T= 2146 K, which is the adiabaticflame temperature.

For this adiabatic combustion process the entropy production is equalto the entropy change of the process and is given by

_Sgen ¼ D _S ¼ �Dmix_Sair þ Dr

_S0298:15 þ

Z T

298:15

Xi

_niCP;i

TdT

þ Dmix_Sproducts

ð8:30Þ

_Sgen ¼ �3:095ð�RSxi ln xiÞair þ ðDrH298:150� DrG0298:15Þ=298:15

þRZ T

298:15

12:035

Tþ 2:976:10�3 þ 0:1848:105

T 3

!dT ð8:31Þ

þ3:595ð�RSxi ln xiÞproductsThe Gibbs energy of the reaction is �228,572 J/mol H2 and is also obtainedfrom the standard tables used before [2].

_Sgen ¼ �3:095:4:273� 44:427þ 8:314 12:035 ln2146

298:15

�

þ2:976:10�3ð2146� 298:15Þ � 0:1848:105

2

1

21462� 1

298:152

� ��þ3:595� 8:314ð0:2782 ln 0:2782þ 0:04172 ln 0:04172

þ0:6801 ln 0:6801Þ ð8:32Þ_Sgen ¼ �13:23� 44:43þ 244:06þ 22:44 ¼ 208:8 W=K ð8:33Þ

Table 1 Coefficients of Eq. (8.27)

Species A B (K�1) D (K2)

N2 3.280 0.593 � 10�3 0.040 � 105

O2 3.639 0.506 � 10�3 �0.227 � 105

H2O 3.470 1.450 � 10�3 0.121 � 105

Chapter 894

This yields for the lost work or lost exergy for this combustion reaction

_Wlost ¼ _Exlost ¼ T0_Sgen ¼ 62:27 kW ð8:34Þ

The exergy flowing in is the sum of the chemical exergy of hydrogen and theexergy value of air at standard conditions. This value is normally chosen tobe 0 J/mol. In our case air was considered to be dry air containing only 21mol% oxygen and 79 mol% nitrogen. The exergy value of air can becalculated from

_Exair ¼ _nairð�xiExchem;i þ RT0�xi ln xiÞ ð8:35Þ_Exair ¼ 3:095ð0:21 � 3:97þ 0:79 � 0:72þ 8:314 � 298:15 � 10�3

ð0:21 ln 0:21þ 0:79 ln 0:79ÞÞ ¼ 0:4 kWð8:36Þ

E _xin ¼ 236:1þ 0:4 ¼ 236:5 kW ð8:37ÞThe exergy flowing out of the system is then calculated from

E _xout ¼ E _xin � E _xlost ¼ 236:5� 62:3 ¼ 174:2 kW ð8:38Þ

The thermodynamic efficiency is therefore 174.2/236.5 = 0.74, or 74%. Theprice of the spontaneous combustion of H2 is the loss of 26% of its originalexergy. The remaining 74% is now available with the form of heat of itscombustion products. As we see from Eq. (8.33), the largest contribution to_Sgen comes from the generation of thermal energy leading to a vast increaseof the temperature. In a fuel cell, operating at a much lower temperature,this entropy generation can be reduced considerably.

REFERENCES

1. Angus, S.; Armstrong, B.; de Reuck, K.M. International Thermodynamic Tables

of the Fluid State-5, Methane, IUPAC data series number 16; Pergamon Press:Oxford, 1978.

2. Smith, J.M.; Van Ness, H.C.; Abbott, M.M. Introduction to Chemical En-

gineering Thermodynamics, 5th ed.; McGraw-Hill: New York, 1996.3. Vargaftik, N.B.; Vinogradov, Y.K.; Yargin, V.S.Handbook of Physical Properties

of Liquids and Gases Pure Substances and Mixtures, 3rd ed.; Begell House Inc.:New York, 1996; 805–854.

4. Hilsch, R. The use of the expansion of gases in a centrifugal field as a coolingprocess. Rev. Scientific Instr. Feb. 1947, 18, 108.

5. Ranque, G. Experiments in a vortex with simultaneous exhaust of hot air and

cold air. Le Journal de Physique et le Radium. June 1933, 4, 1125.6. http://www.twisterco.com.

Simple Applications 95

9Energy Conversion

I hear and I forget.I see and I remember.

I do and I understand.—Confucius

In this chapter we explore how the exergy concept can be used in the analysisof energy conversion processes. We provide a brief overview of commonlyused technologies and analyze the thermodynamic efficiency of (1) combus-tion, (2) a powerplant based on gas turbine technology, (3) a simple steampowerplant, and (4) a combined cycle/cogeneration plant. At the end of thischapter we summarize our findings and make some concluding remarks.

1 INTRODUCTION

The conversion of one form of energy into another has always been vital to theexistence of man; man consumes food to liberate the chemical energy storedtherein by means of oxidation. The discovery of fire by primitive man is agood example of transforming chemical energy present in the wood into heatand allowed man to consume cooked foods and ward off predators. Wind-mills, steam engines, hydroelectric plants, nuclear plants, and so on, all have acommon purpose: the conversion of one form of energy into another.

Now, that energy can be neither created nor destroyed is a well-knownstatement of the principle of conservation of energy and is mathematicallyformulated in the first law of thermodynamics. Thus, if we speak loosely of‘‘energy production,’’we do not mean its production from nothing, since thiswould violate the first law of thermodynamics, but simply the conversion ofone form into another. It is this conversion that is the crux of human existenceon earth today, and civilization as we know it depends entirely on variousforms of energy conversion. The power outages in California in early 2001,

97

and in the northeastern United States and Italy in 2003, highlight the de-pendency of human society on energy. At present, the method of choice seemsto be the use of chemical energy contained in fossil fuels.

Most of our available energy is obtained indirectly from chemicalenergy. In the steam turbine,* the generation of mechanical work proceedsthrough pathway I (Fig. 1) and includes heat and electrical energy, whereasthat of the internal combustion engine does not include electrical energy,which is pathway II [1–3].

Other pathways that involve technology to harness the power of theatom (nuclear fission and fusion) are also used, albeit not (yet?) as widespreadas the aforementioned pathways. At present, anthropogenic nuclear fusionhas not reached technological maturity and, in certain countries, nuclearenergy has a negative image. Pathways that do not involve the generation ofheat also exist, for example, the generation of mechanical work for millingprocesses from wind energy and propulsion from wind energy (in boats) havebeen around for centuries. The use of solar radiation to generate electricity insolar cells in satellites is also a good example, though using solar energy forterrestrial purposes has been increasing since then (see Chapter 15).

In theUnited States alone, approximately 8%of theGDP is used for thegeneration of energy, which amounts to $437 billion [2]. Since at least 1950,industry has been the largest energy-consuming sector in the U.S. economy,although its share has reduced from 47% in 1950 to 37% in 1990 [4]. Thebreakup by energy source is as follows. In the United States, 55% of theelectricity is coal-based, more than twice as much as the next largest source,nuclear power, at 22%. Hydroelectric and alternative power sources such asgeothermal energy generation take up only 10% and 1%, respectively. Interms of energy use by fuel, the list is topped by oil, which contributes to 48%ofU.S. national energy spending, followed by natural gas, at 31%. Oil has the

* The steam turbine provides mechanical energy, which can be transformed into electrical

energy by means of a generator. The advantage of this is that it allows for transportation of

the electricity at high voltages.

Figure 1 Commonly used energy conversion pathways.

Chapter 998

advantage that it has a high energy density (heating value), is liquid, and istherefore easy to transport and can be used in a variety of sectors (transpor-tation, space heating, industrial heating, etc.). Oil, on the other hand, doeshave its problems. Its global distribution is uneven, leading to a concentrationof wealth and power, and can lead to a struggle between those who have andthose who have not. Furthermore, like all fossil fuels (e.g., coal) its productionand use can have environmentally hazardous effects, including the emission ofNOx and SOx and occasional oil spills. Natural gas has become an increas-ingly popular fuel due to its environmental cleanliness. Even though gas fieldswith sour gas are common, the sweetening process is straightforward, asopposed to the ‘‘sweetening’’ of oil or coal.

The Energy Information Administration (EIA), an independent agencywithin the United States Department of Energy, predicted that over the nexttwo decades, the world energy consumption will increase by 59%. The predic-tions are that natural gas will remain the fastest-growing component of con-sumption across the globe, and nuclear generation of electricity is expectedto increase, peaking around 2015. The use of renewables as solar energy andbiomass is expected to increase by 53%, and the largest share of world energyconsumption will continue to be oil [5]. It is well known that the use of fossilfuels results in net emissions of CO2, which in turn are alleged to contributeto enhanced atmospheric levels of this greenhouse gas. Although there is noscientific consensus, increased levels of CO2 could contribute to global warm-ing. It therefore makes sense to examine energy conversion processes for thedevelopment of energy conversion technologies.

As said earlier, the first law of thermodynamics states that energy canbe neither created nor destroyed, but it does not imply that all energy will beconverted into a form that is useful (electricity or mechanical work). Inher-ent in the conversion processes are inefficiencies that disallow the completeconversion into useful forms of energy. It is at this point that the usefulnessof the second law of thermodynamics is clear; the second law of thermody-namics, appropriately paraphrased, states that all real conversion processesare irreversible and therefore contribute to the dissipation of energy touseless forms of energy. As described in earlier chapters, lost work, avail-ability, or exergy analysis, which is an elegant form of analysis based onthe first two laws of thermodynamics, can provide valuable insight into thelocation, origin, and nature of energy conversion inefficiencies and how theycan be alleviated. Making a process more ‘‘energy-efficient’’ is attractivesince it can allow for more useful energy production, that is, conversion intoelectricity or mechanical work.

At the heart of lost work analysis lies the concept that energy can begiven a quality tag, following George Orwell [6], ‘‘All Joules are equal, butsome Joules are more equal than others.’’ This means that one Joule of heat

Energy Conversion 99

at 1000 K is more useful than, say, one Joule of heat at 298 K. This is a directconsequence of the work potential of these heat streams, as stated in Chap-ters 6 and 7, where precise definitions of physical and chemical exergy aregiven. A direct consequence of the second law of thermodynamics is that thework potential (exergy) can never be utilized completely in real processes.Since all real processes are irreversible, every process step will produce afinite amount of lost work, thus diminishing the amount of useful work.

Lost work analysis is useful in analyzing energy conversion processessince it can pinpoint the process step where most work is lost or dissipated.This can provide guidelines for the improvement of the process as a whole.In this chapter, we will examine the generation of electricity from coal andnatural gas, using simple combustion and cogeneration. In Section 2 webriefly survey commonly used power generation technologies and discuss thethermodynamic efficiency of combustion in Section 3. We then move on toSection 4, where we analyze power generation using gas turbines in combi-nation with combustion chambers. A simple steam-based powerplant is ex-amined in Section 5, and in Section 6 a combined cycle and a combined cyclecogeneration powerplant are discussed. We conclude this chapter withSection 7.

2 ELECTRIC POWER GENERATION

Power is defined as the rate at which work is performed [2]. Direct transfor-mation of wind energy tomechanical work is convenient if a milling process isthe user of this energy. In this day and age, however, transformation to elec-trical energy seems to bemore useful, as manymodern instruments depend onelectricity as their energy source.* We must bear in mind that wind energypower generation is dependent on the availability of wind, and, as such,continuous production is not assured. Electric power is commonly generatedusing one of the following technologies/energy sources [2,3,7,8]:

1. Steam plants2. Gas turbines3. Combined cycle4. Nuclear reactors5. Hydrogenerators6. Wind power

*A notable exception is of course the internal combustion engine in automobiles (alluded to

earlier) where locomotion is the primary objective and the chemical exergy of fuel is partly

converted to mechanical work.

Chapter 9100

7. Solar energy8. Geothermal energy

2.1 Steam Plants

In a steam plant, steam is generated by combustion of a fossil fuel, whichreleases the necessary heat. Water is pumped into the boiler, and the heat ofcombustion from the furnace forms wet steam. Directly passing wet steamthrough the turbine could damage the turbine blades as condensation in thefinal stages would inevitably create small droplets. To avoid this, superheatedsteam is created by heating the wet stream even further, which can be passedthrough the turbine. After the turbine, the steam is condensed to water againand reused. A simple schematic of a steam plant is given in Fig. 2 [9,10].

Steam plants usually operate on the Rankine cycle [9,10], as shown inFig. 3. This figure shows the ideal Rankine cycle in the sense that the pumpand turbine operate isentropically, that is, reversibly or without entropy pro-duction. In practice, these will operate with entropy production.

2.2 Gas Turbines

Gas turbines have enjoyed a resurgence in popularity in recent years, mainlydue-to substantial improvements in efficiency [2,3]. Many implementationsare possible for gas turbines, but in its basic configuration, atmospheric airis drawn into a rotary compressor (Fig. 4). The compressed air enters thecombustor, where it mixes with fuel and combustion takes place. The hot

Figure 2 Schematic of a simple steam cycle in a steam plant [3].

Energy Conversion 101

gases subsequently enter a turbine where mechanical work is extracted. Thegases then exit at atmospheric pressure.

The gas turbine process operates on the Brayton cycle, as illustrated inFig. 5 [2,8,9]. The compression reduces the volume and increases the pres-sure. The combustion takes place isobarically. The turbine results in a re-duction of the pressure and an increase in volume of the combustion gases.The combustion gases then leave the turbine at atmospheric pressure. Sincethere is a flow of material into and out of the system, the system is not closedbut constitutes an open system.

2.3 Combined Cycle

The combustion gases that leave the gas turbine still have a great deal ofheat that can be utilized [2,3]. The combined cycle plant does not discard thehot combustion gases directly to the environment, but uses a heat recoverysteam generator and drives a separate steam turbine (Fig. 6).

Figure 4 Schematic of a simple, singe-shaft gas turbine process.

Figure 3 T-S diagram with ideal Rankine cycle.

Chapter 9102

It is understood that the steam exiting the steam turbine is condensedand returned to the boiler in a fashion similar to the steam cycle, as discussedearlier (Fig. 2).

2.4 Nuclear Reactors

Instead of using fossil fuels to generate heat by combustion, which is an exo-thermic chemical reaction, a nuclear reaction can be used to generate the

Figure 6 Schematic of a combined cycle plant.

Figure 5 P-V diagram with Brayton cycle.

Energy Conversion 103

necessary heat. In nuclear powerplants, the heat is generated by nuclearfission. The heat, in turn, is used to generate steam. Broadly speaking, thepressurized water reactor and the boiling water reactor are used in the UnitedStates today [2,3]. In the pressurized water reactor (Fig. 7), water is pumpedthrough the reactor by a reactor coolant pump. This is the last step in theclosed loop, typically referred to as the primary loop. In the secondary loop, afeed water pump circulates water through a heat exchanger where the primaryand secondary loops exchange heat. The water in the secondary loop is turnedto steam here and feeds a turbine, where electricity is generated. In the boiling-water reactor, there is only one loop, and as a result, the overall efficiencies arehigher at the added expense that the turbine becomes radioactive. We will notanalyze the efficiency of nuclear reactors. The interested reader is referred to[11] and [12], where an analysis is presented. The efficiency of the process wasfound to be around 50%, where main losses were due to irreversible heattransfer from the nuclear heat source to the cooling water.*

2.5 Hydrogenerators

Hydrogenerators produce electricity by converting the potential energystored in water to kinetic energy when water is allowed to fall in height

Figure 7 Schematic of a pressurized water reactor [3].

* The assumption is typically made that the nuclear fuel can be treated as a heat source at an

infinite temperature [12].

Chapter 9104

through a turbine. The turbine shaft is generally arranged vertically, as op-posed to the horizontal shafts of the gas and steam turbines. The efficiencyof hydroelectric power generation plants can be estimated to be [11] around80%, which is extremely high. However, when examining the hydroelectricpower station, one must realize that in certain cases the formation of artificiallakes and subsequent flooding of large areas are necessary. This will not showup in a thermodynamic efficiency analysis of the power generation processas such. In the case of the power station at Niagara Falls, no artificial floodingis necessary, and the environmental impact is probably minimal. We will notdiscuss the environmental impact in this chapter and only examine the ther-modynamic efficiency of the process.

2.6 Wind Power

The use of wind energy to generate mechanical work has been known forcenturies and has been used extensively in milling processes. In recent years,the interest in renewable energy has stimulated development in wind-gener-ated electricity. Wind is a resource that is definitely renewable. In the UnitedStates, California is the leader in using wind energy for its power require-ments, and wind energy accounts for more than 1% of the state’s electricityrequirement. This pales in comparison to Denmark, where 12% of the coun-try’s electricity is from wind power,* and goals have been set to 15% by theyear 2005 and 50% by 2050. The current high contribution of wind energyto the Danish national requirement indicates that wind energy is definitelya viable option. In other European countries, such as Germany and TheNetherlands, wind power is becoming increasingly more important.

2.7 Solar Power

At present, the production of power from solar energy is not a significantcontributor-in electricity generation. However, this technology has attractedattention as a potential alternative for future energy production. This isdiscussed in detail in Chapter 15.

2.8 Geothermal Energyy

The presence of geothermal energy is proven by visual evidence by phenom-ena such as volcanic activity, geysers, hot springs, pools of boiling mud, and

*Announced in mid-2000.yAdapted from [13].

Energy Conversion 105

so forth. Over the centuries, man has used this naturally occurring heatsource. The simplest example is probably that of bathing in hot baths fortherapeutic benefits (balneology). Most of these springs in ancient days wereof thermal origin and can still be used even today.

The Maoris of New Zealand used the naturally occurring geothermalphenomena to their advantage. It is not an uncommon sight to see a localfisherman catch fish in a cool river and drop it into a hot pool to cook it.Bathing in the warm pools is also equally common. Although organizedtourism may have had a hand in orchestrating these scenes, nonetheless wemay assume that there is a factual historical basis.

In Iceland almost all buildings are supplied with domestic heat fromgeothermal sources. Few Icelandic houses of less than 40 years of age havechimneys. In short, there are many applications of geothermal heat, of whichwe have only mentioned a small number. Probably the most spectacularadvance for geothermal energy was the production of electricity fromnaturally occurring steam using steam engines in 1904 in Italy. Almost halfa century passed before any other country followed Italy’s pioneering work ingeothermal energy generation. Now, New Zealand, the United States (Cal-ifornia), Italy, and other countries have installed geothermal energy capacity.The production of electric power from geothermal energy is now a well-established activity.

3 COAL AND GAS COMBUSTION

Power generation plants such as the steam plant, gas turbine plant, andcombined cycle plants require combustion of a fossil fuel. Now, combustion isa chemical reaction of fuel with an oxidant (usually oxygen), and it makessense to examine the combustion process more closely and analyze itsthermodynamic efficiency. This means that we will examine the furnace/combustor of Figs 2, 4, and 6.Wewill examine coal and gas combustion at thelevel needed for thermodynamic analysis, after discussing some commonly usedcoal combustion processes.

Coal combustion processes can be classified based on process type (seeTable 1), even though classification based on particle size, flame type,reactor flow type, or mathematical model complexity is also possible [7].

3.1 Fixed or Moving Beds

Combustion of coal in a fixed bed (e.g., stokers) is the oldest and mostcommon method of coal combustion. In recent decades, however, the fixed

Chapter 9106

beds have lost some of their popularity due to the increased use of fluidizedbed and suspended bed combustors [2,7].

3.2 Suspended Beds

In suspended bed or entrained flow reactor technology, the coal is crushed,dried, and then pulverized to fine powder in a crusher and mill. As Table 1shows, the coal particles used in entrained flow reactors are very small. Thepulverized coal is transported with air to the furnace (primary air), and sec-ondary air is heated and fed into the combustor to ensure complete com-bustion. The residence time of the coal in the furnace is typically around 1 to2 sec, which usually suffices for complete combustion. However, not all coalburns completely, and fly ash will be generated (see Table 1).

3.3 Fluidized Beds

The combustion of coal in fluidized beds is becoming increasingly morecommon. Atmospheric fluidized bed combustion (afbc) technology has beenused commercially for the last two decades, whereas pressurized fluidized

Table 1 Classification of Coal Combustion by Process Type

Process type Fixed or moving bed Fluidized bed Suspended bed

Particle size, Am 10,000–50,000 1,500–6,000 1–100Operating

temperature, K<2,000 1,000–1,400 1,900–2,000

Advantages Established technology,low grinding, simple

Low SOx andNOx emissions,less slagging

High efficiency,large-scalepossibilities,high capacity

Disadvantages Emissions, especiallyparticulate, lessefficient than other

methods

New technology High NOx,fly ash,pulverizing

expensiveCommercial

operationsStokers Industrial boilers Pulverizing coal

furnaces and

boilers

Source: Refs. 2 and 7.

Energy Conversion 107

bed combustion (pfbc) is not yet as widespread. A simple schematic of afluidized bed is given in Fig 8.*

At this point, we can start our thermodynamic analysis of combustion.We assume moist bituminous coal with 57.7% carbon, 4.1% hydrogen,11.2% oxygen, 0.7% nitrogen, 1.3% sulfur, 10% water, and 15% ash on amass basis. The work potential or standard chemical exergy value of this typeof coal is 23,583 kJ/kg, as computed by Szargut et al. [11], and its higherheating value (HHV) is 21,860 kJ/kg.y Irreversible combustion and heat trans-fer occur simultaneously in a combustion chamber. For thermodynamiccalculation, we first consider adiabatic combustion followed by heat transfer.The combustion products will be CO2, H2O, oxides of nitrogen and sulfur,

Figure 8 Schematic of a fluidized bed.

*In practice, the gases exiting the fluidized bed reactor contain a certain amount of ash and

have to be cleaned.Also, the combustion products of coal are sometimes corrosive, whichmeans

that in addition to air being fed into the reactor, various other chemicals are added to ensure

‘‘clean’’ combustion products that will not corrode turbine blades or violate environmental

standards. Coal combustion is a very active field of research, and many exciting developments

are occurring there. In this analysis, we make certain assumptions that illustrate the

thermodynamic concepts as clearly as possible. Therefore, we do not examine the effect of

hydrodynamics, heat, andmass transfer, which are very important in the combustion of the coal

particle and the distribution of combustion products. We do not expect that this will have a

significant impact on the analysis.yThe higher heating value gives the gross heat content for the fuel, including the heat of vapor-

ization, and is commonly used in the United States. In Europe, the lower heating value is often

used, which does not include the heat of condensation [2].

Chapter 9108

and nitrogen, assuming that air is used for combustion. Now, the usefulproduct is the heat, which is generated by the exothermic chemical reaction(combustion), and not the combustion products. At this point, we canevaluate the process. Consider one kg/sec of coal that is combusted with anadequate amount of air (approximately zero exergy contribution). The rate atwhich work potential (exergy) flows into the system is therefore 23,583 kW.The combustion releases heat, namely at a rate of 21,860 kW at a temperatureT. Since we have created a heat source at temperature T, it is straightforwardto compute the work potential (exergy) of this heat source. All we need to do ismultiply the heat release rate (21,860 kW) by the Carnot factor 1 � (T0/T).This means that if the combustion takes place at temperature T, the efficiencyof the combustion alone is Dcombustion= (21,860/23,583) [1� (T0/T)]=0.93 [1� (T0/T)]. From Table 1, we can choose a ‘‘typical’’ operating temperature of1200 K, assuming we use a fluidized bed. This means that the thermodynamicefficiency of the combustion equals Dcombustion = 0.93 [1 � (298.15/1200)] =0.7! This means that already 30% of the maximum work has been lost! Wesummarize this simplified analysis in Fig. 9.

The heat is available at 1200 K, but there will be temperature differ-ences in the heat exchanger, so more available work will be lost in the heatexchange process. What can we learn from this example? If we examine theCarnot factor, the answer seems to be clear. If we increase the operatingtemperature of the combustor, we can increase the efficiency and lose lesswork in the process. For example, if we had chosen an operating tempera-ture of 2000 K, as could be possible in the suspended bed, we would have

Figure 9 Flow of exergy in fluidized bed combustion.

Energy Conversion 109

obtained an efficiency of 0.79, which is quite considerable. However, anygain in efficiency could be offset by the increase in work necessary to pul-verize the coal! For the sake of simplicity, we have not included these in thisanalysis. From the point of view of efficiency of combustion, the higher thecombustion temperature, the better. This would of course mean that steamcould be generated at higher temperatures or pressures, which is a directtechnological consequence provided suitable materials are available. Notethat since combustion is a spontaneous reaction, some work potential isimmediately lost, as discussed in Chapter 4.

We caution the reader that applying Carnot’s analysis is based on theassumptions that the heat is available at temperature T and that the heatreservoir is infinite. This means that if we use the adiabatic flame tempera-ture for T, we will end up with a maximum attainable efficiency, since ex-change of heat will inevitably lead to a reduction in the temperature of thereservoir. From our analysis it is not clear whether we used an adiabatic flametemperature. However, we can safely state that at least 30% of the maximumwork potential has been lost.Wewill return to this subtle point at a later stage,when we examine the combustion of natural gas.

If a fossil fuel is combusted in a steam plant, the combustion proceeds torelease thermal energy and uses this energy to supply the heat used to generatesteam. The analysis given above can be adapted to any type of (fossil) fuel. Ingas turbines, the combustion takes place for a different reason, namely toproduce high-velocity gases. Gas turbines are frequently used since the inlettemperatures can be much higher than the maximal steam temperatures, andcurrently inlet temperatures around 1400 K are commonplace. However, inorder to use a gas turbine, expansion to a lower pressure has to occur. This isthe reason that both the fuel and air have to be elevated in pressure at roomtemperature. A typically used pressure is 2.1 MPa, and after combustion thepressure typically had dropped to about 2.0 MPa. The expansion toatmospheric pressure occurs at high temperatures, and because of theelevated temperatures, the volume of the gas that will undergo the expan-sion is much larger than the volume of gas initially compressed, thus leadingto a net production of mechanical energy. Consider Fig. 4. Air enters thecompressor at ambient conditions and is compressed to some higher pressure.No heat is added, but the temperature of the air rises due to compression,which means that the temperature and pressure of the compressor dischargeare higher than at the inlet.

Upon leaving the compressor, the compressed air enters the combus-tor, where fuel is injected and combustion takes place. The combustionprocess takes place at essentially constant pressure. In the turbine section, partof the energy of the hot gases is converted into work. This conversion takesplace in two steps. The hot gases are expanded, a portion of the thermal energy

Chapter 9110

is converted into kinetic energy, and the kinetic energy into an increase in theenthalpy which can be converted into work. Some of the work developed bythe turbine is used to drive the compressor. Typically, more than 50% of thework is used to drive the compressor, which generally includes compressorefficiencies.

We will now consider the combustion of one mole per second ofnatural gas (we assume 100% methane). The heating value of methane (seeChapter 6) is almost equal to its work potential or exergy value [11,14]. Forthe sake of simplicity in the ensuing analysis, we will set this work potentialvalue of the gas to be equal to the energy value or, equivalently, the value ofthe heat of reaction. In Table 2, we have tabulated the exergy of methane ata number of different conditions.

As the table shows, the exergy is not a strong function of temperature orpressure. For the illustrative purposes of our analysis, we use the value of831.6 kJ/mol. We assume that the oxygen from the air (assumed to be 20%mol oxygen and 80% nitrogen for simplicity) and the methane react asfollows:

CH4 þ EO2 þ 4EN2 �! 2H2Oþ CO2 þ 4EN2 þ ðE� 2ÞO2 ð1Þwhich is essentially complete oxidation. We will assume E > 2, so completecombustion takes place, and we will also assume a feed rate of 1 mol methaneper second. Table 3 shows the prodxuct distribution in the gas flowing out ofthe combustor.

The work potential of the ambient air is nearly zero, will be small for thecompressed air flowing into the combustor compared to the work potential ofthe fuel, and can be neglected [when chemical transformations take place, thebulk of the exergy (work potential) is usually due to the chemical componentof the exergy].

In adiabatic combustion the chemical energy of the natural gas is con-verted into the same amount of thermal energy stored in the effluent stream.For the effluent stream, however, the exergy content or available work will no

Table 2 Standard Exergy Value of Methaneat Different Conditions

Substance Ex, kJ/mol

CH4 (1 bar, 298.15 K) 831.6CH4 (100 bar, 298.15 K) 842.6CH4 (100 bar, 373.15 K) 842.9

Source: Ref. 14.

Energy Conversion 111

longer be equal the energy content, since some work would have been lost.(See Fig. 10. The numbers are calculated in the following section.)

We can compute E since we made the assumption that the combustionis adiabatic. At this point we invoke the first law for flowing systems, whichreduces to

DH: ¼ 0 ð2Þ

because no work is performed in the combustor, and no heat exchange takesplace (adiabatic). This means that the sum of the rate of enthalpy change ofreaction and the enthalpy change of the combustion gases equals zero. Thisequation can be written as

�DrH: ¼ n

:Z T3

T2

CpðTÞdT ¼ n:CpðTmÞðT3 � T2Þ ð3Þ

where n is the number of moles* in the combustion stream and approximatethe molar heat capacity of the mixture Cp(Tm) by evaluating Cp at a meantemperature. For convenience and mathematical simplicity we use thearithmetic mean, though this is formally incorrect, but it simplifies ourcalculations greatly without adding unnecessary complications to the com-putations. For a better andmore accurate method of calculating this integral,we refer to standard textbooks on thermodynamics. The temperatures T3

and T2 denote the outlet and inlet temperatures of the combustor, respec-tively. Here, we assume an inlet temperature of T2 = T1 = 298.15 K and an

Table 3 Product Distribution in Combustion Gas

Species

Number of moles

per second Gas mole fraction, yi

H2O 22

5Eþ 1

CO2 11

5Eþ 1

N2 4E4E

5Eþ 1

O2 (E�2) E� 2

5Eþ 1

* In our example n = 5E+1.

Chapter 9112

outlet temperature of 1423.15 K, which is a common inlet temperature forthe gas turbine [9]. We therefore compute the heat capacity at (1/2)(298.15+1423.15) = 860.65 K.

Table 4 shows the value of the heat capacity at 860.65 K for the con-stituents of the effluent stream.

This yields Cp = Si yiCp,i = (63.1+159.8E)/(5E+1). If we insert thisinto Eq. (3), and substitute the heat of reaction and the values of T3 and T2,we obtain

ð1423:15� 298:15Þ � ð63:1þ 159:8EÞ5Eþ 1

� ð5Eþ 1Þ ¼ 831:6� 103 ð4Þ

which yields E = 4.23. We can compute the work potential of the gaseouseffluent, by using the definition

Ex: ¼ Ex

:ph þ Ex

:ch þ Ex

:mix ð5Þ

where the chemical exergy of the stream can be computed as (using Table 5)

Ex:ch ¼ 2ExchðH2OÞ þ 16:92ExchðN2Þ þ ExchðCO2Þ þ 2:23ExchðO2Þ ¼ ð6Þ

Ex:ch ¼ 2� 9:5þ 16:92� 0:72þ 19:9þ 2:23� 3:97 ¼ 59:9 kW

Figure 10 Flow of exergy in adiabatic gas combustion.

Table 4 Heat Capacity ofCombustion Products at 860.65 K

ComponentCp (860.65 K)J mol�1K�1

H2O 39.4

CO2 51.5O2 33.6N2 31.55

Energy Conversion 113

and the mixing contribution as

Ex:mix ¼ n

:RT0

Xi

yi ln yi

¼ 22:1 RT0½0:09 ln 0:09þ 0:05 ln 0:05þ 0:76 ln 0:76

þ 0:10 ln 0:10� ¼ �20:4 kW

ð7Þ

The computation of the chemical exergy of water requires some explanation.It is not equal to zero, since the water in the steam is not in the liquid phase,but in the vapor phase. Therefore, we computed it as

ExgchðH2OÞ � ExlchðH2OÞ ¼ RT0 lnP0

PsatH2O

!

¼ 8:314� 298:15� ln1:013� 105

3:166 � 103� �

¼ 8:6 kJ=mol

Since Exlch(H2O) = 0.9 kJ/mol, this yields Exgch(H2O) = 9.5 kJ/mol. Thephysical exergy rate can be expressed as

Ex:ph ¼ n

: ðDH� T0DSÞ ð8Þwhere DH and DS are the enthalpy and entropy increase of changing a moleof combustion gas from T0, P0 to T, P. From C�engel [9], we take P= 14 barand T = 1150jC = 1423.15 K, which is a common inlet gas condition ofturbines. The quantities DH and DS can be calculated by integrating stan-dard thermodynamic relations and the assumption that the gas behavesideally with constant Cp:

DS ¼Z T;P

T0;P0

dS ¼ Cp

Z lnT

lnT0

d ln T� R

Z lnP

lnP0

d ln P ð9Þ

DH ¼Z T;P

T0;P0

dH ¼ Cp

Z T

T0

dT ð10Þ

Table 5 Standard Chemical Exergyof Selected Components

Component Exch kJ mol�1

H2O (1) 0.9

CO2 19.9O2 3.97N2 0.72

Chapter 9114

where we use the value of Cp = 33.4 kJ/mol.K, computed earlier. Exph cannow be computed:

DH ¼ Cp

Z T

T0

dT ¼ CpðT� T0Þ ¼ 33:4ð1423:15� 298:15Þ

¼ 37:5kJ=mol ð11Þ

DS ¼ Cp

Z lnT

lnT0

d ln T� R

Z lnP

lnP0

d ln P

¼ Cp lnT

T0� R ln

P

P0¼ 33:4 ln

1423:15

298:15� 8:314 ln

14

1ð12Þ

¼ 30:3 J=mol:K

which yields the physical exergy rate

Ex:ph ¼ 22:15ð37:5� 298:15� 30:3� 10�3Þ ¼ 630:5 kW ð13Þ

The total value of the work potential flowing out is 630.5 + 59.9 � 20.4 =670 kW. The amount of work potential flowing in is equal to 831.6 kW, sothe efficiency of this combustion is 0.81 (see Fig. 10). Now, if we use themethod described for the coal combustion, we can also compute thethermodynamic efficiency of the combustion:

Dcombustion ¼ 1� T0

T

� �¼ 1� 298:15

1423:15¼ 0:79 ð14Þ

which is close and can be considered to be the same, considering theapproximations we made! Now, this is no coincidence, because we havesimply computed the thermodynamic efficiency in two different ways. Theanalysis shows that if a higher combustion temperature can be used, theprocess will be more efficient. This can be accomplished by using less air, sothe hot stream is less diluted. These two examples highlight that (complete)combustion, or direct spontaneous reaction, is a process that is limited in itsefficiency. We point out that in fuel cells, or indirect reactions, Carnotlimitations are not present, but other irreversibilitiesmay reduce the efficiency.A discussion of fuel cells is beyond the scope of this book, but we believe thatthis technology will become increasingly more popular and common.

At this point it is useful to point out that simply computing theefficiency based on the Carnot factor is an exercise that should be performedwith care. The Carnot factor, C, is given by C = 1 � (T0/T). As shown inthe example, we can compute the group –CDrH / Exin to get the efficiency!Strictly speaking, this is not always true, but why? The answer is very subtle.Carnot’s analysis holds only for infinite heat reservoirs, and if the heat(which can be viewed as the useful product) is transferred, the temperature

Energy Conversion 115

of the reservoir (the product mixture) also changes! So the correct way ofcomputing the efficiency based on the heat is to take into account the factthat the temperature T is not constant, but is variable and will decrease toT0:

Ex: ¼Z T0

T

dEx:Q ¼Z T0

T

1� T0

T

� �dQ: ¼Z T

T0

n:Cp 1� T0

T

� �dT ð15Þ

Note that we have used dQ: ¼ �n:CPdT to ensure that when heat is

transferred out of the ‘‘reservoir,’’ the temperature of the reservoir de-creases. Closer inspection of this equation reveals that it can be simplified asfollows:

Ex: ¼Z T

T0

n:Cp 1� T0

T

� �dT ¼

Z T

T0

n:CpdT� T0

Z T

T0

n:Cp

TdT

¼ n: ½DH� T0DS� ð16Þ

This is the definition of the physical exergy of the effluent stream! Compu-tation of the terms will yield the physical component of the stream, andcombination with the chemical and mixing components will allow for thecomputation of the efficiency. The question now remains, why did compu-tation of the efficiency based on the Carnot factor give the correct number?The answer is that since the temperature of the effluent gases is fixed, itmimics an infinite heat reservoir, and therefore n

:[DH � T0DS] simplifies to

n:DH½1� T0ðDS=DHÞ� ¼ n

:DH½1� ðT0=TÞ� , since DG ¼ DH� TDS ¼ 0 at

equilibrium.

4 GAS TURBINE

We can make an estimate of the efficiency of a powerplant using a gasturbine (see Fig. 4). We assume that the combustor inlet temperature of thegases is T2 = 298.15 K and turbine inlet temperature of T3 = 1423.15 Kand use the data from the methane combustion example. We further assumethat the turbine has a total efficiency of 0.75. We will first compute theturbine work if the expansion is isentropic to 1 bar. Consider Eq. (9), wherewe set DS = 0. We can derive the following [10]:

T4

T3¼ P4

P3

� �R=Cp

ð17Þ

We can solve this equation iteratively (CP is a function of the arithmeticmean temperature) to obtain T4 = 747.5 K, which is the isentropic exit

Chapter 9116

temperature and yields CP = 34.07 J/mol.K. The isentropic work rate isgiven by

W:s ¼ �n:DH ¼ �n:CpðT4 � T3Þ ¼ 22:1� 34:07ð1423:15� 747:5Þ¼ 508:992 kW

ð18Þ

If we assume a turbine efficiency* of 0.75, the ‘‘real’’ work becomes508.9�0.75=381.675 kJ, and the exit temperature can be computed to be892.1 K. Now in general, around 50% of the work generated by the turbineis used to drive the compressor, which means that the net generation ofelectricity is only 0.5 � 381.657 = 190.8 kJ. This means that the total systemhas a thermodynamic efficiency of 190.8/831.6 = 0.23! Now the hot gasstream allowed to exit the system at 892.1 K still has work potential. We cancompute the total exergy rate by the method described earlier:

Ex: ¼ Ex

:ph þ Ex

:ch þ Ex

:mix ð19Þ

Since the composition did not change, we do not need to recompute Exchand Exmix. We need to recalculate Exph since the temperature is different.

*An increase in efficiency of the turbine is extremely important for the overall result, and a

great deal of research is directed to improving this. Discussion of this, however, is beyond the

scope of this book.

Figure 11 Thermodynamic efficiency in a gas cycle.

Energy Conversion 117

We compute CP at 595.13 K, which is the arithmetic mean of 892.1 K and298.15 K, to obtain 33.104 J/mol.K. In this fashion, we obtain DH =19,662.12 J/mol and DS = 36.28 J/mol.K, which yields the rate Ex

:ph =

n:(DH � T0DS) = 195.47 kW, which in turn gives the rate Ex

:=225.1 kW

(see Fig. 11). In terms of the initial input rate of work potential (830.1 kW),this is 27.1%, which means that 0.271 is going to waste! If this hot gaseousstream could be used somewhere, the efficiency could be increased. We shallexamine this later in Section 6, after we have studied the steam powerplant.

5 STEAM POWERPLANT

Steam powerplants are commonplace in the power-generating industry. Con-sider Fig. 2 and Fig. 12, where the heat is generated in the burner.

State-of-the-art first law efficiencies of boilers are typically between85–90%, that is, the fraction of fuel energy value (heat of combustion) cap-tured in steam. It is not surprising that the efficiency is not 100%, since theflue gas that exits the boiler is hot and therefore takes with it some of theenergy (‘‘heat goes up the chimney’’). Typical conditions in a steam cycle areas given in Table 6 [3,10].

In Table 6, we have not included the exergies of the fuel, since we willperform our analysis based on 1 kJ/s fuel feed rate. Now, assume the firstlaw efficiency of the boiler is 87%. This means that 1 kJ/s of fuel is fed into

Figure 12 Computation of the thermodynamic efficiency in a steam cycle.

Chapter 9118

the boiler, and 0.87 kJ/s is absorbed in the enthalpic value of steam. Thismeans that the steam rate equals the following:

m:steam ¼ 0:87

h1 � h4¼ 0:87

3; 391:6� 203:4¼ 2:73� 10�4 kg=s

The steam production allows for the computation of the exergy flow atvarious points. For example, the exergy flow at point (1) is simply 2.73 �10�4 � 1402.8 = 0.38 kJ/s. The exergy value of the flue gas stream (5) iscomputed by using the first law efficiency and realizing that the flue gasstream is a heat stream being discarded:

ð1� 0:87Þ 1� 298:15

366:15

� �¼ 0:043kJ=s

Table 7 shows the exergy streams (based on 1 kJ/s exergy input by fuel), whichare calculated by multiplying the exergy values by the steam production.

Now, the maximum amount of work the turbine can extract from thesteam is given by the difference of the exergy streams flowing in and out ofthe turbine (which represent the work potential of the steam), which is 0.38� 0.04 = 0.24 kJ/s. Assuming a turbine efficiency of 75%, we readily see

Table 6 Typical Process Conditions in Steam Cycle

Point Thermodynamic state T, P Exergy (kJ/kg)

(0) Gas + solid/gas + liquid — —(1) Superheated vapor 500 jC, 8600 kPa 1402.8

(2) Wet vapor, quality = 0.9378 45 jC, 10 kPa 149.5(3) Saturated liquid 45 jC, 10 kPa 11.8(4) Subcooled liquid 45 jC, 8600 kPa 12.8(5) aGas 93 jC, 101 kPa —

a We have given the computation of the rate of exergy lost through this stream in the text.

Table 7 Exergy Streamsfor Steam Cycle

Point Exergy (kJ/s)

(0) 1.0(1) 0.38

(2) 0.04(3) 3.2214 � 10�3

(4) 7.6 � 10�4

(5) 0.043

Energy Conversion 119

that 0.24 kJ/s electricity is generated. Therefore, the exergetic efficiency ofthe steam powerplant is 24% if the electricity input of the pump is not takeninto account. The pump duty can be calculated (per unit mass steam) byusing the enthalpy of water: Wpump = h4 � h3 = 203.4 � 191.8 = 11.6 kJ/kgsteam or, equivalently, 3.17 J/s for an ideal pump, by multiplying by thesteam rate. Using an efficiency of 75%, the ‘‘real’’ pump duty equals 4.2 J/s.The new exergetic efficiency is still 24%. We note that the thermodynamicefficiency (second law) of the boiler-furnace 38% is in contrast to the first lawefficiency of 87% (see Fig. 12).

6 COMBINED CYCLE AND COGENERATION

In the direct combustion of fuels in combustion chambers, as described ear-lier, the work is produced by the gases in the turbine. However, the gasesleaving the turbine are still sufficiently hot to be useful (i.e., to have workpotential). For instance, gases exiting the turbine typically have temperaturesof around 800 K [9], which means that this heat has a quality (see Section 6.3)of 1 � 300/800 = 0.625, which is fairly significant. For this reason, practicalpower generation plants usually have heat recovery systems that eitherpreheat the gases flowing into the combustor or generate steam. This steamcan then be used to drive a steam cycle and, after losing much of its quality,can be used in district heating. This is the principle of cascading. Powerplantsthat use a gas turbine and a steam cycle are referred to as combined cycleplants, since they use two cycles for the generation of power (see Fig. 6). Inaddition to using two cycles, a powerplant can also generate heat, which is auseful product.* In the power industry, the simultaneous generation of heatand power is referred to as cogeneration. Consider the gas turbine example.There was waste heat, which was discarded to the environment. Suppose weuse the waste heat to drive a steam cycle. The steam cycle described abovegenerates steam at 500jC (= 773.15 K) from liquid water, supplied at 45jC(318.15 K). To do this, h1 � h4 = 3391.6 � 203.4 = 3187.6 kJ/kgsteam arenecessary. At our disposal is a gas stream (22.1 mol/s) at 892.1 K. We willassume that we cool the gas stream from 892.1 K to 373.15 K (we choosethese temperatures arbitrarily for illustrative purposes only). We computethe average CP of the gas stream at 632.65 K, to obtain 35.36 J/mol.K. The

*Approximately 46% of all energy use in residential buildings goes to space heating and 15%

goes to water heating, whereas for commercial buildings these figures are 31% and 4%,

respectively. This means that low-quality heat can definitely be used, instead of using

electricity or fossil fuels for heating purposes.

Chapter 9120

heat transferred is therefore equal to 22.1 � 35.36 (892.1 � 373.15) = 405.5kJ/s, which means that the work the steam turbine can generate is 405.5 �0.24 = 97.32 kJ/s. So the combined cycle generates 97.32 + 190.8 = 288.12kJ/s. The net efficiency of the combined cycle is therefore 302.4/831.6 = 0.35.Now in practice, combined cycle plants have efficiencies of around 0.5. Thereason we did not recover this value is that we simply pasted two cyclestogether, while in practice the conditions are chosen carefully to optimizepower output. However, the concept is clear: Combined cycles have higherefficiencies. If we now turn this ‘‘combined cycle’’ plant into a cogenerationcombined cycle plant, we use the heat as a useful product. The heat isavailable at 373.15 K. We consider only the physical component-of theexergy Ex

:ph = n

:(DH � T0DS). We can compute DH, DS using the standard

methods described earlier to obtain DH=2977.5 J/mol, DS=8.91 J/mol.K,which gives the rate Ex

:ph= 7.1 kJ/s. The new efficiency is now 0.373, which is

an improvement on the original figure. Note that sometimes heat is used as astarting point that yields different (first law) efficiencies. We prefer to use thework potential (exergy) to avoid ambiguity.

7 CONCLUDING REMARKS

We presented thermodynamic analyses of some simple power generationtechnologies. The analysis hinted that the combustion could be made moreefficient in certain cases by using higher temperatures. The boiler in thesteam cycle had a fairly low efficiency (0.38), which meant that the overallefficiency of the steam cycle was low as well. The reason that the boiler had alow thermodynamic efficiency is that steam is generated at 500jC, whereasthe heat is available at higher temperatures; in other words, the heat transferis across a large temperature difference, which reduces the efficiency.

Other noteworthy points are that electricity requirements of the pumpin the steam cycle (incompressible fluid) are less important than the require-ments of the compressor in the gas turbine cycle (compressible fluid) andthat inefficiencies in the latter can reduce overall thermodynamic efficiency agreat deal.

The combined cycle and the combined cycle cogeneration plantshowed that waste heat could be put to good use, thus generating less lostwork. The process conditions used in the analysis of the combined cycleplant were chosen for illustrative purposes and were arbitrary. In practice,the conditions are generally chosen to increase power output. (See, forexample, Chapter 5 on maximum power output.)

We wish to alert the reader that in the analyses presented above, theresults were essentially independent of the type of fuel used. From an

Energy Conversion 121

efficiency point of view this may be true, but from a sustainability point ofview this is not. In general, gas is a much cleaner burning fuel than coal andrequires less pre- and posttreatment. Even though the standard power gener-ation plants can be made more efficient using thermodynamic analysis (lostwork, availability, or exergy analysis), we note that power generation basedon fossil fuels is not sustainable since combustion of these leads to increasedCO2 levels, depletion of finite resources, and alternatives such as hydroelec-tric, solar power energy, and so on should be considered if man is to live in atruly sustainable society. The necessary tools and insights are developed inSection III.

REFERENCES

1. McDougal, A. In Fuel Cells; John Wiley & Sons: New York: 1976.2. Encyclopedia of Chemical Technology; Kroschwitz, J.I., Howe-Grant, M., Eds.

Interscience Publishers: New York: 1991; Vol. 20.

3. Energy Technology and the Environment; Bisio, A., Boots, S., Eds. WileyEncyclopedia Series in Environmental Science: New York:1995; Vol. 2.

4. U.S. Department of Energy, Energy Information Administration. Annual En-

ergy Review 1991, DOE/EIA-0384(91), Washington, DC, June 1992.5. Energy Information Administration, Office of Integrated Analysis and Fore-

casting, U.S. Department of Energy, International Energy Outlook 2001, DOE/ELA-0484, 2001. Available online from the Department of Energy Web site at

ftp://ftp.eia.doe.gov/pub/pdf/international/0484(2001).pdf.6. Orwell, G. Animal Farm. Harcourt, Brace, and Company: New York, 1946.7. Energy Technology and the Environment; Bisio, A., Boots, S., Eds. Wiley

Encyclopedia Series in Environmental Science: New York, 1995; Vol. 1.8. Energy Technology and the Environment; Bisio, A., Boots, S., Eds. Wiley

Encyclopedia Series in Environmental Science: New York, 1995; Vol. 3.

9. C�engel, Y.A.; Boles, M.A. Thermodynamics—An Engineering Approach, 2ndEd.; McGraw-Hill: New York, 1994.

10. Smith, J.M.; Van Ness, H.C.; Abbott, M.M.; Van Ness, H. Introduction to

Chemical Engineering Thermodynamics, 6th Ed.; McGraw-Hill InternationalEditions: New York, 2000.

11. Szargut, J.; Morris, D.R.; Steward, F.R. Exergy Analysis of Thermal, Chemical,and Metallurgical Processes. Hemisphere Publishing Corporation: New York,

1988.12. Pruschek, R. Brensst Warme Kraft 1970, 22, 429.13. Armstead, H.C.H. Geothermal Energy: Its Past, Present and Future Contribu-

tions to the Energy Needs of Man; E. & F. N. Spon: London, 1983.14. Smoot, L.D. In Fossil Fuel Combustion: A Science Source Book; Bartok, W.

Sarofim, A.F., Eds.; John Wiley & Sons, Inc.: New York, 1991.

Chapter 9122

10Separations

In this chapter we examine the thermodynamic efficiency of the propane–propylene separation process by distillation. The tools necessary for thisanalysis are developed using the first and second laws of thermodynamics.Sources of thermodynamic inefficiency are pinpointed and, finally, someoptions are discussed to improve the efficiency of the separation.

1 INTRODUCTION

Operations that deal with the separation of mixtures into pure componentshave long been part of industry. For example, distillation has played a veryimportant role in both the chemical and petrochemical industries. Crystalli-zation has been used for centuries in refining sugar in the food industry, and itis also frequently encountered in the pharmaceutical industry. Stricterdemands on product quality have forced industries to devise complicatedseparation units and, as a result, separation processes, now more than ever,play a central role in industry. To get an idea of the importance of separationprocesses, it makes sense to study some of the statistics [1]. Distillationconsumes over $6 billion of U.S. energy annually, which amounts to 3% ofthe national total. For chemical plants, one third of the typical capitalinvestment is meant for separation units. For petroleum refineries andbiochemical factories, this is typically 70%. Since separations are importantconsumers of energy, it makes sense to make efforts to reduce this energyconsumption. Reduced energy consumption will, in general, lead to less costand less burden on the environment, resulting in a more sustainable society.As an example, we will consider the distillation of propane and propylene [5],

123

the raw material for polypropylene. The model used will contain somesimplifying assumptions to illustrate the concepts clearly.

2 PROPANE, PROPYLENE AND THEIR SEPARATION

Propane is a colorless, easily liquefied, gaseous hydrocarbon, the third mem-ber of the paraffin series followingmethane and ethane. The chemical formulafor propane is CH3CH2CH3. It is separated in large quantities from naturalgas, light crude oil, and oil-refinery gases and is commercially available asliquefied propane or as a major constituent of liquefied petroleum gas (LPG).

As with ethane and other paraffin hydrocarbons, propane is animportant raw material for the ethylene petrochemical industry. The decom-position of propane in hot tubes to form ethylene also yields another im-portant product, propylene. The oxidation of propane to compounds such asacetaldehyde is also of commercial interest.

Propylene is used principally in organic synthesis to produce the follow-ingmaterials: acetone, isopropylbenzene, isopropyl alcohol, isopropylhalides,and propylene oxide. Propylene is also being polymerized to form polypro-pylene. A colorless, flammable, gaseous hydrocarbon, propylene, also calledpropene, has the chemical formula (CH2jCHCH3) and is obtained frompetroleum; large quantities of propylene are used in themanufacture of resins,fibers, elastomers, and numerous other chemical products. Although propyl-ene is an important rawmaterial in the chemical industry, it is produced almostexclusively as a byproduct in steam cracking and in catalytic cracking [2].

In general, a C3 stream is obtained that contains propane, propylene,propadiene, and propyne, and these are separated in a C3 distillation column,also referred to as the C3 splitter. Propane–propylene separation and, as arule, olefin–paraffin separation, are energy-intensive, and some estimates arethat 1.27� 1017 J are used for olefin–paraffin separation on an annual basis [3]while roughly 3% is used by paraffin–olefin distillation columns [4]. Thisprovides an incentive to examine the propane–propene separation, which isan example of paraffin–olefin separation.

Propane and propylene have similar atmospheric boiling points (pro-pane: �42.1jC, propylene, �47.70jC) and, as a result, separation of thesecompounds requires highly complicated units. Distillation is by far the mostcommonly used separation process in the chemical industry today. Thevariants in use are

1. Single-column process2. Double-column process3. Heat pump process

Chapter 10124

2.1 Single-Column Process

This process requires a large number of trays (150–200), resulting in units ofabout 100 m. The reflux can be condensed with cooling water (columnpressure 16–19 bar) or in air coolers (column pressure 21–26 bar).

2.2 Double-Column Process

For the large throughputs that are common today, the double-columnprocess is preferred over the single-column process, since it does requiresmaller columns with smaller column diameters, which makes transporta-tion of these units easier. A simplified schematic of the double-columnprocess is given in Fig. 1. Only the reflux from the second column iscondensed with cooling water. The pressure of the first column is sufficientlyhigh (ca. 25 bar) that the overhead vapors (ca. 59jC) can be condensed inthe reboiler of the second column and serve as the heat carrier. Heating thefirst column with steam is not necessary, and warm water can be used forheating purposes. Both columns provide approximately half the propeneproduct. Since the reboiler for the second column also serves as thecondenser of the first column, the first column does not require any coolingwater. As a result, the cooling water requirements are about half that of thesingle-column process.

Figure 1 Schematic of double-column process. (Adapted from [2].)

Separations 125

2.3 Heat Pump Process

In the aforementioned process, the heat for the reboiler is usually available aswaste heat from the steam cracker, for example, and is essentially cost-free. Ifthis heat is not available, a heat pump can be used. A schematic of the heatpump process is given in Fig. 2. The overhead vapors are heated slightly in thereflux subcooler, which enables these vapors to be compressed and cooled inthe condenser-reboiler.

In the example we present below, we restrict ourselves to the single-column process for the simple reason that the analysis is straightforward andillustrates the concepts best. In addition, data for this analysis are readilyavailable [6].

3 BASICS

As stated earlier, distillation is a widely used separation technique for liquidmixtures or solutions. Formation of these mixtures is straightforward, and isusually spontaneous, but the separation of a mixture into its separateconstituents requires energy. One of the simplest distillation operations* isflash distillation. In this process, part of the feed stream vaporizes in a flashchamber, and the vapor–liquid mixture, which is at equilibrium, is separated.

Figure 2 Schematic of heat pump process. (Adapted from [2].)

* For a detailed discussion of distillation, we refer to textbooks on the subject (see, e.g., [7]).

Chapter 10126

The vapor is rich in the more volatile component, but complete separation isusually not achieved. A simple schematic showing the necessary equipmentfor flash distillation is given in Fig. 3.Wewill illustrate the concepts by using asimple case of flash distillation of a binary mixture.

The feed, at temperature T0 and pressure P0, and mole fraction z, entersthe system. It is elevated to a higher pressure and temperature by a pump andheat exchanger, both requiring input of energy. The binarymixture, now atTF

and PF, proceeds to a valve, which reduces the pressure, and the mixtureseparates into a vapor and a liquid phase, which are separated physically inthe flash vessel. The resulting vapor effluent is rich in the volatile component,and the liquid stream is lean in the same.

Figure 4 shows how the separation can be visualized in a phase diagram,in this case a Pxy-diagram atT1. The feed, with composition z, is initially atTF

and PF. The pressure is then reduced (the ‘‘flash’’), which results in the feed’schanging pressure and temperature toT1 andP1. The trajectory of this changein the phase space is given by the dotted line, since the starting condition (TF,PF) is not in the Pxy-diagram at T1. The equilibrium state at TF and PF is thatof a vapor–liquid mixture, and the feed phase separates into a vapor and aliquid at composition yV and xL, respectively, if equilibrium is reached.

Standard mass and energy balances can be derived for the flashdistillation system. We will make the simplifying assumption that thermody-namic equilibrium is reached in the flash vessel. We write the mass and energybalances for the control volume denoted by the dashed box in Fig. 3.

Figure 3 Schematic representation of equipment necessary for flash distillation.

Separations 127

The overall mass balance reads

F ¼ Vþ L ð1Þand the component mass balance for the most volatile component is

Fz ¼ VyV þ LxL ð2ÞThe energy balance can easily be shown to be

FhF ¼ VhV þ LhL ð3Þwhere the hF, hV, and hL are the enthalpies of the feed, the vapor, and liquidstreams, respectively. The flash drum is taken to be well insulated, so theflash process can be treated as adiabatic.

These equations can be solved simultaneously to yield

� L

V¼ yV � z

xL � z¼ hV � hF

hL � hFð4Þ

In an enthalpy-composition diagram, this represents a straight linethrough coordinates (hV, yV) representing the vapor and (hL, yL), whichrepresents the liquid (Fig. 5). The branch denoted ‘‘vapor enthalpy’’ showsthe enthalpies of saturated vapors at their dew points as function of the vaporcomposition ( y). The branch marked ‘‘liquid enthalpy’’ shows the enthalpiesof saturated liquids at their bubble points as a function of the liquidcomposition (x). Since we are assuming that the vapor and liquid are atequilibrium, the line connecting L and V is a tie line.

Figure 4 Pxy diagram of a binary flash distillation at constant temperature.

Chapter 10128

We can describe binary distillation in a similar way. We will brieflyreview some of the main concepts regarding distillation relevant to ourdiscussion. For further information and details regarding distillation, thereader is referred to books ondistillation (e.g., [7]).With distillation, the feed isintroduced more or less centrally into a vertical cascade of trays. The sectionabove the feed is typically referred to as the absorption, enriching, or rectifyingsection, while the section below the feed is called the stripping or exhaustingsection (see Fig. 6). The column has N trays or stages, where the numberingtypically starts at the top of the column and ends at the bottom tray.

The vapor flow Vi from tray i has composition yi and goes to tray i-1,whereas the liquid flow Li leaving tray i goes to tray i+1 and has thecomposition xi. Now consider a typical tray in the enriching section as shownby control volume I in Fig. 6. The mass and energy balances for this controlvolume are

Vjþ1 ¼ Lj þD ð5ÞVjþ1yjþ1 ¼ Ljxj þDzD ð6Þ

Vjþ1hV; jþ1 ¼ LjhL; j þDhD þQout þQloss;1 ð7Þwhere Qout is the cooling load of the condenser and Qloss,1 is the heat lost dueto imperfect thermal insulation of the enriching section, which we assume, for

Figure 5 Schematic representation of an enthalpy-composition (Hxy) diagram andyx projection for vaporization.

Separations 129

simplicity, to be equal to zero.We can solve these equations simultaneously toobtain

Lj

Vjþ1¼ zD � yjþ1

zD � xj¼

Qout

Dþ hD � hV; jþ1

Qout

Dþ hD � hL; j

ð8Þ

Similarly, for tray k in the stripping section (control volume II, Fig. 6 weobtain

Lk

Vkþ1¼ ykþ1 � zB

xk � zB¼

hV;kþ1 þ Qin

B� hB

hL;k þ Qin

B� hB

ð9Þ

where the overbar is used for L andV to denote that these are quantities in thestripping section that are not necessarily equal to those in the enrichingsection. We now make the following assumptions:

1. The specific heat changes are negligible compared to latent heatchanges.

2. The heat of vaporization per mole is constant.

Figure 6 Schematic representation of a distillation column.

Chapter 10130

These conditions, in addition to the condition of adiabatic operationof the column, are known as the constant molar overflow conditions, whichimply that L, V, L, andV are constant. Therefore, Eqs. (8) and (9) can bewritten as

L

V¼ zD � y

zD � xð10Þ

L

V¼ y� zB

x� zBð11Þ

where we only consider the first equalities of the aforementioned equationsand have suppressed the subscripts. These two equations are the top andbottom operating lines that can be used in the graphical McCabe–Thielemethod to determine the number of equilibrium stages.

Now, the operating line for the feed tray is the same as the operating linefor flash vaporization, Eq. (4), which is usually written as

y ¼ � LF

VFxþ F

VFð12Þ

which can be written in terms of the fraction remaining liquid

q = (LF)/(F ) = (hV�hF)/(hV�hL) as

y ¼ q

q� 1xþ 1

q� 1zF ð13Þ

Figure 7 shows how these operating lines can be used to determine thenumber of ideal stages in a binary distillation column. The reflux is defined as

Figure 7 The McCabe–Thiele diagram to determine the number of ideal stages.

Separations 131

the fraction distillate that flows back to the column: r= L0/D. We can readilycompute the reflux ratio. Consider Eq. (5), with j = 0:

V1 ¼ L0 þD ð14ÞWe can divide L0 by the left-hand side and right-hand side of this

equation to obtain

L0

V1¼ L0

L0 þD¼

L0D

.L0

D

.þ 1¼ r

rþ 1ð15Þ

By the constant molar overflow assumption, we can write this as

L

V¼ r

rþ 1ð16Þ

In case of the propane–propylene separation, the y= x line and the yx-equilibrium line are very close, as shown in Fig. 8. This means that a largenumber of trays is necessary, which is the case in practice. Another conse-

Figure 8 The yx diagram for propane–propene at 16 bar.

Chapter 10132

quence of the close proximity of the y= x line and yx-equilibrium line is thatthe slope of the top operating line, L /V , will be close to unity. This impliesthat the reflux ratio will be high and the condenser will have to ‘‘liquefy’’ largeamounts of vapor, leading to a large duty.

4 THE IDEAL COLUMN: THERMODYNAMIC ANALYSIS

As stated earlier, the separation of mixtures into their constituents requiresenergy. In distillation this energy is supplied as heat. To this end, it is useful torecall that Carnot (see Chapter 3 for details) showed that the maximumamount of work that can be extracted from a heat source Q at T > T0 withrespect to the surroundings at T0 is given by

Wmaxout ¼ Q 1� T0

T

� �ð17Þ

It is straightforward to show that if heat is available at temperaturelevelsTh andTl, the maximum amount of work that can be extracted from theformer temperature level isWout

max=Q[1� (T0)/(Th)], whereasWoutmax=Q[1�

(T0)/(Tl)] is the maximum amount of work for the latter. From this, it can beshown that if heat flows spontaneously from a temperature level Th to atemperature level Tl (with Th > Tl > T0), the amount of available work thathas been lost is given by

Wlost¼ QT0

1

Tl� 1

Th

� �ð18Þ

which is the difference of the maximum amounts of work available at the twotemperature levels. If, on the other hand, heat at a temperature level Tl has tobe upgraded to a level Th, the minimum amount of work required is

Wminin ¼ QT0

1

Tl� 1

Th

� �ð19Þ

Another useful equation is the Clausius–Clapeyron equation. It statesthat, provided the ideal gas law holds and the enthalpy of vaporization, DvH,is independent ofT (which is a reasonable assumption for a small temperaturerange), the slope of the vapor pressure curve is given by

d ln psat

d 1T

¼ � DvH

Rð20Þ

Separations 133

where R is the gas constant and psat is the vapor pressure. Consider two verysimilar components, propylene [1] and propane [2], with close boiling points.The ideal relative volatility is now defined as

aideal12 upsat1

psat2

ð21Þ

From Eqs. (20) and (21) it follows that over the temperature range ofdistillation

lnaideal12 ¼ � DvH

R

1

Tbottom� 1

Ttop

� �ð22Þ

where Tbottom and Ttop denote the temperatures at the bottom and top of thecolumn, respectively. At this point, it is useful to note that the assumptions wehave made are that (1) the mixture is ideal, which is an approximation of thebehavior of the real mixture, and (2) the enthalpy of vaporization is the samefor both components. In reality, the relative volatility a12 will differ slightlyfrom the ideal value. A simplified scheme for the separation of an equimolarmixture of propylene and propane is given in Fig. 9. The feed is a liquidmixture introduced at that point where the liquid has the same compositionand temperature.

Per mole of feed F, the distillate D amounts to 1/2 mole and so does thebottom product B, since the feed is equimolar. With a reflux ratio r= L/D, inwhich L is the number of moles of liquid reintroduced at the top of the

Figure 9 Distillation at reflux ratio r (rmin<r<l).

Chapter 10134

column, L = rD = 1⁄2r moles above the feedpoint and (1/2r + 1) below thefeedpoint. The vapor flow V = 1/2(r+1) throughout the column. The heatintroduced at the bottom of the column is therefore

Qin ¼1

2ð1þ rÞDvH ð23Þ

We assume that the heat of vaporization is roughly the same for bothcomponents and that the temperature dependence is negligible over the rangeof the column. From this, it follows that

Qin ¼ Qout ð24Þin which Qout is the cooling duty of the condenser. Now, it is interesting tonote that the overall separation does not require any energy! The number ofJoules entering the column equals the number of Joules leaving the column,which is a direct consequence of the first law of thermodynamics. However,the ‘‘quality’’ of these heat streams or, equivalently, the available work ofthese heat streams, is not the same, due to the Carnot factor, the term inbrackets in Eq. (17), which is due to the second law of thermodynamics. In anideal column, that is, a column operating under reversible conditions, the heatis stripped of its quality and ‘‘pays’’ for the separation of the liquid mixtureinto its constituents in the liquid state. The minimum work required toseparate the liquid mixture into its constituents is given below (see Fig. 10):

W idealsep ¼ �RT0

Xi

xiln xi ð25Þ

Figure 10 Minimum work required to upgrade the quality of heat.

Separations 135

where the assumption ismade that themixture behaves in an ideal fashion andis close to the temperature of the surroundings, which, for the propane–propylene mixture, is a fair assumption. If we further insert the assumptionthat the mixture is equimolar, Eq. (25) reduces to

W idealsep ¼ RT0 ln 2 ð26Þ

which is the minimum amount of work that needs to be introduced into thecolumn.

According to Eq. (19),

Wminin ¼ Qmin

in T01

Ttop� 1

Tbottom

� �ð27Þ

which has to equal the minimum amount of work that has to be spent onthe separation:

Wminin ¼W ideal

sep ð28ÞThis also defines the minimum reflux ratio, r, according to

Qminin ¼

1

2ðrmin þ 1ÞDvH ð29Þ

Equations (22), (26), (27), and (29) can be combined to yield

rmin ¼ 2 ln 2

ln aideal12

� 1 ð30Þ

We stress that this equation dictates the minimum reflux ratio basedpurely on thermodynamic arguments. As a12

ideal= 1.11 in our case, the value ofrmin=12.28. In general, themixture will not be equimolar, and if the productsare not pure but satisfy a less strict specification, the value of rmin will besmaller. Now, a column operated under these conditions will have anefficiency of 100% since it is using the minimum amount of work necessaryto separate the components.

5 THE REAL COLUMN

The previous analysis begs the following question. What will the efficiency beof a ‘‘real’’ propane–propylene distillation column? To answer this question, wemust realize that heat cannot be transferred into the column without a finitetemperature difference. In a ‘‘real’’ column with less stringent product qualityconstraints, the heat is supplied atTR=377K, the bottom temperature of the

Chapter 10136

column isTb=331K, the temperature at the top of the column isTt=320Kand this heat is transferred to the surroundings at T0= 298K [6], as shown inFig. 11. The minimum heat required for separation is, according to Eq. (29),

Qminin ¼

1

2ðrmin þ 1ÞDvH ð31Þ

with rmin = 9.64 from the data in [6]. The separation inside the column doesnot take place according to thermodynamic ideal processes, and the real heatinput is larger:

Qrealin ¼

1

2ðr real þ 1ÞDvH ð32Þ

where rreal = 15.9.At the bottom of the column, the heat has to be transferred over a

temperature difference of 377–331 = 46 K, and the resulting lost work caneasily be calculated with Eq. (18). Then the heat flows from 331 K to 320 Kinside the column and is used to perform the separation. Finally, the heat isdiscarded at the top of the column at 320 K to the surroundings at 298 K.

Figure 11 Important temperatures for the distillation column.

Separations 137

The overall thermodynamic efficiency of the column can be computed asfollows:

goverall ¼Qmin

in D1

T

� �column

T0

Qrealin D

1

T

� �bottom

þD 1

T

� �column

þD 1

T

� �top

" #T0

ð33Þ

which yields Doverall = 0.093! This means that the thermodynamic efficiency ofthe distillation column is only 9.3%. Closer scrutiny of Eq. (33) reveals thatthe main sources of inefficiency are the temperature-driving forces in thecondenser and reboiler (the ratio Qin

min/Qinreal equals 0.63 and reflects work

losses inside the column). We can visualize the sources of inefficiency bytracking the fate of heat that enters the separation process at the reboiler. Theheat,Qin

real, is supplied atTR, whichmeans that the available work (the exergy)of this heat isQin

real [1� (T0)/(TR)]. Since the heat enters the column at Tb, theavailable work of the heat entering the column is Qin

real [1 � (T0)/(Tb)]. So theamount of work lost in the heat transfer process in the reboiler equalsWlost =Qin

real T0 [(1)/(Tb) � (1)/(TR)]. Similarly, the amount of work available in heatleaving the column isQin

real [1� (T0)/(Tt)]. Now, the amount of work lost in thecolumn is not the difference of the work available in the heat flowing in andout of the column. The heat is used to separate the propane and propene. Theminimum amount of work necessary to achieve this separation is, accordingto Eq. (27),

Wminin ¼ Qmin

in T01

Tt� 1

Tb

� �So, the amount of work lost in the column is given by

Wlost ¼ Qrealin T0

1

Tt� 1

Tb

� ��Qmin

in T01

Tt� 1

Tb

� �We can summarize these findings in a table, Table 1.

Table 1 Overview of Exergy in Distillation Column

Exergy in Exergy out Exergy lost

Reboiler Qrealin 1� T0

TR

� �Qreal

in 1� T0

Tb

� �Qreal

in T01

Tb� 1

TR

� �

Column Qrealin 1� T0

Tb

� �Qreal

in 1� T0

Tt

� �ðQreal

in �Qminin ÞT0

1

Tt� 1

Tb

� �

Condenser Qrealin 1� T0

Tt

� �Qreal

in 1� T0

T0

� �Qreal

in T01

T0� 1

Tt

� �

Chapter 10138

We can scale the results by dividing all the results by the total exergyinput Qin

real [1 � (T0)/(TR)] to obtain Table 2, where we use the data and Eqs.(31) and (32).

As Table 2 clearly shows, the sum of the lost work (lost exergy) equals0.907 in scaled form, which means the thermodynamic efficiency is 1–0.907=0.093, or 9.3%, as we obtained earlier. Themain sources of inefficiency are the

Figure 12 Ultimate fate of one unit of exergy in distillation column: 9.3% is usedfor the separation; 32.8% is lost in the condenser; 52.5% is lost in the reboiler, and5.4% is lost in the column.

Table 2 Overview of Exergy in Distillation Column in Scaled Form

Exergy in Exergy out Exergy lost

Reboiler

Qrealin 1� T0

TR

� �Qreal

in 1� T0

TR

� � ¼ 1:00

Qrealin 1� T0

Tb

� �Qreal

in 1� T0

TR

� � ¼ 0:475

Qrealin T0

1

Tb� 1

TR

� �Qreal

in 1� T0

TR

� � ¼ 0:525

Column

Qrealin 1� T0

Tb

� �Qreal

in 1� T0

TR

� � ¼ 0:475

Qrealin 1� T0

Tt

� �Qreal

in 1� T0

Tb

� � ¼ 0:328

ðQrealin �Qmin

in ÞT01

Tt� 1

Tb

� �Qreal

in 1� T0

TR

� � ¼ 0:054

Condenser

Qrealin 1� T0

Tt

� �Qreal

in 1� T0

TR

� � ¼ 0:328

Qrealin 1� T0

T0

� �Qreal

in 1� T0

TR

� � ¼ 0:00

Qrealin T0

1

T0� 1

Tt

� �Qreal

in 1� T0

TR

� � ¼ 0:328

Separations 139

heat transfer in the reboiler and condenser, which contribute to 0.525+ 0.328= 0.853 units of lost work (see Fig. 12).

6 EXERGY ANALYSIS WITH A FLOW SHEET PROGRAM

To obtain the thermodynamic efficiency it is not necessary to perform theanalysis as shown above.We can easily estimate the thermodynamic efficiencyby setting up an available work or exergy balance (see Fig. 13). We begin bydefining our control volume. In this case, we choose the volume to include thereboiler, the column, and the condenser. The propane–propene feed entersthe control volume and, with it, exergy enters as well (ExF). Exergy also entersthe system at the reboiler in the form of heat (ExQ1). Exergy flows out of thesystem with the distillate (ExD), the bottoms product (ExB), and as ‘‘heat’’rejected at the condenser (ExQ2).

In the hypothetical case that the process is reversible in the thermody-namic sense, the flow of exergy into the system will equal the flow of exergyout of the system. But since real processes always have a degree of irrevers-ibility, some exergy is lost (Exlost). We can now set up the exergy balance:

ExF þ ExQ1 ¼ ExB þ ExQ2 þ ExD þ Exlost ð34ÞBecause chemical transformation does not occur, we do not need to

include the chemical exergy in the exergy flows.We can nowwrite expressions

Figure 13 Schematic representation of the exergy flow in a separation process.

Chapter 10140

for the terms in the exergy balance (Table 2) based on one mole feed enteringthe system for both the reversible and real separation process.

Note that for both the reversible and irreversible, real, processes we areonce again invoking the assumption that the mixing behavior is ideal, thusthat there is zero enthalpy of mixing, and the ideal entropy of mixing. Inflowsheeting programs, it is very simple to extract the values of the enthalpiesand entropies of the streams entering a process unit, as is the heating andcooling duty. It is then straightforward to compute the exergy of these streamsfor the real process case.

Note that the ExQ1 and ExQ2 terms differ for the reversible andirreversible cases. The reversible case has the minimum heat input Qin

min attemperature levelTb since heat is transferred reversibly without a temperaturegradient. Similarly, it is rejected at Tt. It is in these two terms that thereversible and irreversible exergy balances differ. Now first consider thereversible exergy balance, where Exlost is, by definition, equal to zero. FromEq. (34), using the expressions in Table 3 for the reversible case, we obtain

1

2hC¼3 þ hC3

� �� T0ðsC¼3 þ sC3

� ��� 1

2hC¼3 þ hC3

�� T0 sC¼3 þ sC3

� �� �� ��0

� RT0ln2þQinmin 1� T0

Tb

� �¼ 1

2hC3� T0sC3

ð Þ � 1

2hC3� T0sC3

ð Þj0 ð35Þ

þ 1

2hC¼3 � T0sC¼3� �� 1

2hC¼3 � T0sC¼3� �j0 þQin

min 1� T0

Tt

� �

Table 3 Overview of Exergy Streams for Reversible and Real Processes

Reversible Real

ExF 1=2ððhC¼3þ hC3

Þ � T0ðsC¼3þ sC3

ÞÞ 1=2ððhC¼3þ hC3

Þ � T0ðsC¼3þ sC3

ÞÞ

�1=2ððhC¼3þ hC3

Þ � T0ðsC¼3þ sC3

ÞÞj0

�RT0 ln 2

�1=2ððhC¼3þ hC3

Þ � T0ðsC¼3þ sC3

ÞÞj0

�RT0 ln 2

ExQ1 Qinmin 1� T0

Tb

� �Qin

real 1� T0

TR

� �

ExB 1=2ðhC3� T0sC3

Þ � 1=2ðhC3� T0sC3

Þj0 1=2ðhC3� T0sC3

Þ � 1=2ðhC3� T0sC3

Þj0

ExQ2 Qinmin 1� T0

Tt

� �Qin

real 1� T0

T0

� �

ExD 1=2ðhC¼3� T0sC¼

3Þ � 1=2ðhC¼

3� T0sC¼

3Þj0 1=2ðhC¼

3� T0sC¼

3Þ � 1=2ðhC¼

3� T0sC¼

3Þj0

Separations 141

which is the exergy balance for the reversible separation process. Similarly, weobtain the following balance for the real process:

1

2ððhC¼3 þ hC3

Þ � T0ðsC¼3 þ sC3ÞÞ � 1

2ððhC¼3 þ hC3

Þ � T0ðsC¼3 þ sC3ÞÞj0

� RT0 ln 2þQinreal 1� T0

TR

� �¼ 1

2ðhC3� T0sC3

Þ� 1

2ðhC3� T0sC3

Þj0 ð36Þ

þ 1

2ðhC¼3 � T0sC¼3 Þ �

1

2ðhC¼3 � T0sC¼3 Þj0 þ Exlost

Note that the ExQ2 = 0 for the real case, since heat is rejected at T0.Upon simplification, Eq. (36) yields, after combination with Eq. (35),

Exlost¼ �QinminT0

1

T0� 1

TR

� ��Qin

realT01

Tt� 1

Tb

� �ð37Þ

Exlost can now be calculated in scaled units (that is, per unit exergyinput):

Exlost

QinrealT0

1

T0� 1

TR

� �¼ 1�Qin

minT01

Tt� 1

Tb

� �Qin

realT01

T0� 1

TR

� � ð38Þ

which upon substitution of the data yields 0.907, or equivalently, a thermo-dynamic efficiency of 0.093 = 9.3%, which is in agreement with the earliervalue. In this case, we also could have obtained an estimate of the lost work(lost exergy) by substituting values from a flowsheeting program into the realexergy balance, Eq. (36). The only quantities necessary for this computationare (1) the heating duty of the reboiler and (2) the enthalpies and entropies ofthe entering and exiting stream at the process conditions and the base state,which are all readily available! We stress that since the control volume waschosen to include the distillation column, the reboiler, and the condenser, thethermodynamic calculation yields a net thermodynamic efficiency and anestimate for the total lost work. If information regarding the separate units(i.e., reboiler, column, and condenser) is desired, the control volume should bechosen differently. For example, by choosing the control volume to onlyinclude the reboiler, the efficiency of the heat transfer process can becomputed. Because we already have computed the fraction of work usedfor the separation and lost in the reboiler, column, and condenser (Fig. 12), itis not necessary to compute these. As said earlier, the main sources of thelosses are the reboiler and the condenser. Both the reboiler and condenser loseconsiderable amounts of work due to the heat transfer over large temperaturedifferences (Table 2). A simple way of improving these heat transfer processesis therefore, to reduce these temperature–driving forces. A noteworthy point

Chapter 10142

is, however, that the heat for the reboiler is supplied at 377 K, which is oftenavailable as waste heat in a chemical plant. Because waste heat is usuallyrejected (hence the term ‘‘waste’’) heat integration could improve the processefficiency and reduce total exergy losses for the entire chemical plant (see Fig.14). Now, what Fig. 14 shows is that heat integration can sometimes reducethe exergy losses of a chemical plant as well as reduce the need for utilities such

Figure 14 Schematic representation of the effect of heat integration on lost exergy(lost work).

Figure 15 Hybrid distillation of propane–propene.

Separations 143

as steam. In the particular case of the propane–propene single-columndistillation, waste heat is frequently used to satisfy the heating duty of thereboiler.

We wish to point out that another way to improve the single-columnprocess is to use a membrane to split the feed into two different feed streams(see Fig. 15). Since the membrane does part of the separation, the column hasto do less work to complete the separation, whichmeans less reboiler duty andless stages [8]. Figure 16 shows a ‘‘cartoon’’ of the y–x projection of thesystem, including the operating lines. The membrane splits the feed in twostreams, which enter the column at different feed locations. The operatinglines are lowered in the region around the feed, resulting in a reduction of thereflux ratio and the number of stages. We wish to point out that other ways ofimproving efficiency of distillation columns in general may include thefollowing:*

1. State-of-the-art control to ensure operation at the specified designconditions. Proper control can allow for operation with a smaller‘‘safety margin.’’

2. Preheat the feed using waste heat instead of adding extra heat tothe reboiler that operates at a higher temperature level.

Figure 16 yx projection for a hybrid distillation process.

* The options we enumerate for improving efficiency of a column are by no means exhaustive

or unique. We simply state them here to alert the reader of possible improvement options. We

note that ‘‘cookbook’’ techniques to improve efficiencies are foredoomed to obsolescence

since technology advances and they do not capture ‘‘out-of-the-box’’ solutions, which can

shift paradigms.

Chapter 10144

3. Reduce the pressure drop in the column by using packings insteadof trays, if possible.

4. Use intermediate condensers and reboilers (if possible). This pushesthe operating lines closer to the equilibrium line (Fig. 17), thusreducing inherent column inefficiencies. The use of waste heat mayalso be possible nowwithout upgrading to the reboiler temperature.A potential disadvantage may be that extra trays are needed.

5. Separate to lower purity, and continue separation with otherseparation techniques.

7 CLOSING REMARKS

The analysis presented in this chapter is an example of how the principles ofthermodynamics can be applied to establish efficiencies in separation units.We have shown how exergy analysis or, equivalently, lost work or availabilityanalysis can be used to pinpoint inefficiencies in a distillation column, whichin this case were the temperature driving forces in the condenser and thereboiler. The data necessary for this analysis can easily be obtained fromcommonly used flowsheeters, and minimal extra effort is required to computethermodynamic (exergetic) efficiencies of various process steps. Use of hybriddistillation has the potential to reduce column inefficiencies and reducenumber of trays. We note that for smaller propane–propene separation

Figure 17 yx projection for a distillation process with intermediate condenser and

reboiler.

Separations 145

facilities (less than 5000 bbl/day [9]), novel technologies such as adsorptionand reactive distillation can be used.

REFERENCES

1. Separation Technology. Li, N.N., Strathmann, H., eds. United Engineering Foun-dation, 1987.

2. Ullmann’s Encyclopedia of Industrial Chemistry. VCH Publishers, Inc.: New

York, 1993; Vol. A22.3. Humphreys, J.L.; Seibert, A.F.; Koort, R.A. Separations Technologies Advances

and Priorities; U.S. Department of Energy Report 12920–1, 1991.

4. Gokhale, V.; Hurowitz, S.; Riggs, J.B. A comparison of advanced distillationcontrol techniques for a propane/propene splitter. Ind. Eng. Chem. Res. 1995,34, 4413–4419.

5. de Swaan Arons, J.; van der Kooi, H.J. The Thermodynamic Analysis of Dis-

tillation, Some Parallels with Living Systems, (course for industry organized byProf. Ohe, Science University of Tokyo), Tokyo, Dec., 1999.

6. Seader, J.D. Thermodynamic Efficiency of Chemical Processes; The MIT Press:

Cambridge, Mar 1982.7. Seader, J.D.; Henley, E.J. Separation Process Principles; John Wiley and Sons:

New York, 1997.

8. Pressly, T.G.; Ng, K.M. A break-even analysis of distillation-membrane hybrids.AIChE J. 1998, 44, 93–105.

9. Eldridge, R.B. Olefin/paraffin separation technology: A review. Ind. Eng. Chem.

Res. 1993, 32, 2208–2212.

Chapter 10146

11Chemical Conversion

This chapter examines two industrial polymer processes. Thermodynamicanalysis is used as a tool to locate, in a matter-of-fact fashion, processinefficiencies. Some sample process improvement options are discussed.

1 INTRODUCTION

Chemical industry owes its existence to society’s need for various products.Chemical industry can be viewed as a system, which converts various rawmaterials into useful and waste products, using energy, and sometimesproducing energy (Fig. 1).

At this point we will introduce our working definition of sustainability.Sustainability is defined as the use of resources no faster than they are regen-erated and releasing pollutants to no greater extent than natural resourcescan assimilate them. This definition will be refined later but will suffice forthe moment.

Within the frameworkof sustainability anddurable technology, it is easyto generalize this concept to include chemical industry. Figure 1, albeit rathernaıve, provides a simple framework to start the discussion of how a chemicalprocess can bemademore sustainable. Reduction of energy inputs can lead toa more sustainable chemical industry, as does reduction of waste streams.Exergy analysis can help provide insights into how the process can be mademore energy-efficient, but does not, in general, provide an answer as to howwaste streams can be reduced. Catalysts with higher specificity or careful usefor, and processing of the ‘‘waste’’ products are a better answer to that query.

This chapter gives the example of an exergy analysis of two low-density polyethylene (LDPE) production processes, namely the high-pres-sure and the gas-phase processes. Section 2 provides a general overview ofsome existing polyethylene processes. Section 3 develops some of the toolsnecessary to estimate exergies of polymers. The actual result of the exergy

147

analysis for the high-pressure process is given in Section 4, and some processimprovement options are discussed in Section 5. Section 6 presents theexergy analysis of the gas-phase process followed by process improvementoptions in Section 7. We conclude with a brief summary in Section 8.

2 POLYETHYLENE PROCESSES: A BRIEF OVERVIEW

Polyethylene* (PE) is the largest synthetic commodity polymer in terms ofannual production and is widely used throughout the world in a variety ofapplications. Based on the density, PE is classified as low-density polyeth-ylene (LDPE) at 0.910– 0.930 g/cm3, high-density polyethylene (HDPE) at0.931– 0.970 g/cm3, and linear low-density polyethylene (LLDPE) based on

Figure 1 Abstract representation of chemical industry.

* As the title of this section already suggests, this is only a very brief survey of the commonly

used PE production processes. A detailed description of the processes, the kinetics, and so on

shall not be given, as this is not relevant within the framework of this case study.

Chapter 11148

the polymer chain microstructure. At present, processes that produce PE usethe following raw materials:

Ethylene (for homopolymers)Ethylene and a-olefins (for co-polymers)

The main reaction to obtain homopolymers* from ethylene can be depictedas follows:

nCH2CH2 ! ½CH2CH2�nThe transformation can be achieved in a number of ways. PE is commer-cially produced exclusively by means of continuous processes. The oldestprocess, due to ICI, is the so-called conventional high-pressure process. Inthe 1950s Prof. Ziegler developed special catalysts that made it possible topolymerize ethylene at lower pressures. Since then, many new processes havebeen developed. On the basis of polymerization mechanisms and reactorconfigurations, the PE processes can be classified broadly in five categories,as shown in Table 1.

Among these polymerization processes, the gas-phase process is themost recent addition to the list. Since its emergence, the process has chal-lenged many other existing technologies for market share. In addition todifferences between the gas-phase process and the high-pressure free radicalprocess shown in Table 1, more differences can be noted, which are shown inTable 2. Because the high-pressure process is well-established technology,

Table 1 Polymerization Processes and Reactor Operating Conditions

Conventional

HP

HP bulk

process

Solution

process

Slurry

process

Gas-phase

process

Reactor type Tubular

or autoclave

Autoclave CSTR Loop or

CSTR

Fluidized bed

or stirred bed

Pressure, atm. 1200–1300 600–800 f100 30–35 30–35

Temperature, jC 130–350 200–300 140–200 85–110 80–100

Mechanism Free radical Free radical/

coordination

Coordination Coordination Coordination

Location of

polymerization

Monomer

phase

Monomer

phase

Solvent Solid

surface

Solid

Product grades LDPE LDPE/HDPEa HDPE/LDPE HDPE LDPE/HDPE

a High-pressure plants have been modified to produced HDPE.

Source: Ref. 1.

*The reaction to obtain co-polymers is analogous.

Chemical Conversion 149

and the gas-phase process is a relatively new process with certain advan-tages, we have chosen these two processes as examples for the application ofour thermodynamic analysis.

2.1 Polyethylene High-Pressure Tubular Process

The high-pressure (HP) tubular process is, as stated earlier, a continuousprocess and has been in use for decades in the chemical process industries. Asimplified version of a generic HP tubular process is given in Fig. 2 [1].

A primary compressor increases the pressure of the entering ethylenegas (and propylene gas, which is added as a molecular weight control agent)from between 5 and 15 bar to about 250 bar. The secondary compressorfurther increases the gas pressure from 250 bar to the desired reactor pressure(approximately 2500 bar). An initior is added to the gas as it enters the re-actor. The reactor is operated to ensure a per-pass conversion of 15 to 35%and is a wall-cooled reactor where the cooling water can be used to producesteam. The reaction mixture then enters the high-pressure separator (f250bar), where the mixture is flashed to produce two distinct phases: a poly-ethylene-(PE) rich melt phase and an ethylene-rich gas phase. The separatedgas then enters the recycle loop. The ethylene gas is cooled before enteringthe secondary compressor. The PE enters the low-pressure separator. Thislow-pressure separator, also referred to as a hopper, performs the final de-gassing step. The separated ethylene gas is cooled and some components are

Table 2 Comparison of High-Pressure Free Radical Process andLow-Pressure Gas-Phase Process

High-pressure process Low-pressure process

High energy requirement Low energy requirementHigh capital cost Low capital costLimited to low-density PE Can produce both high- and low-

density PENo co-monomer required(homopolymer) for LDPEproduction

Up to 10–15% co-monomer required(in case of co-polymer)

Catalyst is less sensitive to impurities in

feedstock

Catalyst is very sensitive to impurities

Low raw material costHigher raw material cost

Can produce ethylene and vinyl acetate

co-polymer with long chainbranching

Currently a limited range of co-monomers, mainly linear polymer

chains with short chain branching

Chapter 11150

removed. This step takes place in the low-pressure return gas loop. Thehopper also functions as a storage buffer before the PE enters the extruder.

The extruder granulates the PE. In addition to this function, variousquality enhancers can be added to obtain certain polymer properties, andthe PE is further degassed. The granulation is achieved by pressing the hotPE melt through a perforated plate, directly cooling with water and cuttingthe solidified PE. The water–PE mixture is then led to a separator in whichthe water is removed from the PE. The PE is then dried, bagged, and readyfor transport.

2.2 Polyethylene Gas-Phase Process

Gas-phase polymerization processes, as mentioned earlier, are also used. Inthis section we will discuss a plant geared toward production of LLDPE. Asimplified version of the flow diagram is given in Fig. 3 [1].

Themonomer ethylene is first led through a series of dryers (not shown),mixed with recycle gas, hydrogen, and butylene, and enters the fluidized bedreactor (R1) at the bottom. Catalyst is added from numerous locations onthe side of the reactor (not shown). The reactor operates at approximately85jC and 20 bar (the temperature depends on the desired grade). The heatof reaction is removed as sensible heat of the gas stream and by evaporation

Figure 2 Simplified flow diagram of high-pressure LDPE process.

Chemical Conversion 151

of the partially liquid reaction mixture. The reactor gas exists the top of thereactor.

The gaseous reactor exit stream is compressed (C1) and cooled (H1)and recycled to the bottom of the reactor. The product is removed from thebottom end of the reactor and is led to the polymer discharge vessel (V2).The polymer is discharged to the purge vessel (V3). Nitrogen is passedthrough the polymer in this vessel to remove any remaining gas in the inter-stices of the polymer particles, as well as to purge any of the monomers leftin the solid. The polymer then proceeds to the finishing section. In thissection, additives are added to the product in an extruder. The product ispelletized, bagged, and stored in a warehouse.

3 EXERGY ANALYSIS: PRELIMINARIES

In order to perform an exergy analysis, it is vital to have accurate infor-mation regarding the physical and chemical exergies of the various processstreams. The first is accomplished by having an accurate flow sheet of theprocesses, which readily gives the enthalpies and entropies of the streams ifproper care has been taken in selecting thermodynamic models. This allows

Figure 3 Simplified flow diagram of a gas-phase polymerization process.

Chapter 11152

for the computation of the physical exergy for liquid–vapor mixturesaccording to:

E _xph ¼ D0! actual_LXni¼1

xihli � T0

Xni¼1

xisli

!þ _V

Xni¼1

yihvi � T0

Xni¼1

yisvi

!" #

ð1Þwhere _L = liquid molar flow rate, _V = vapor molar flow rate, xi = liquidmole fraction, and yi=vapor mole fraction. In general, a flowsheetingprogram can give the total entropy and enthalpy of the stream, in whichcase the physical and mixing exergies can be computed as

E _xph ¼ _L Hl � T0SlÞ þ _VðHv � T0S

v� �� �"_LXni¼1

xihli � T0

Xni¼l

xisli

!P0;T0

þ _VXni¼1

yihvi � T0

Xni¼1

yisvi

!P0;T0

# ð2Þ

The computation of the chemical exergy of the various streams is achievedby using documented values of the chemical exergy [2] of the chemicalspecies or from estimation methods [2]. The chemical exergy values used forthe calculations are given in Table 3.

Detailed Aspen (version 9.2) flowsheets were created to simulate (1)the production of 39% crystalline PE from solely ethylene as monomer for

Table 3 Values of Chemical Exergyfor Species

Compound Exch (kJ/mol)

Ethylene 1361.1

Nitrogen 0.72Ethane 1495.8Hydrogen 236.1

Polyethylenea 4650 � 103

Butylene 2659.7Butane 2805.8

a Calculated using group contribution meth-

ods and accounting for crystallinity of PE [3].

Source: Ref. 2.

Chemical Conversion 153

the LDPE HP process, and (2) LLDPE (92 wt % ethylene and 8 wt % 1-butylene). At this point we point out that due to the proprietary nature ofthe analysis and results, some details will be omitted.

4 RESULTS OF THE HP LDPE PROCESS EXERGYANALYSIS

The results of the exergy analysis of the HP LDPE process are given in Fig. 4in the form of a Grassmann diagram, which shows the flow of exergy in theprocess.

The efficiency of the high-pressure LDPE process is 91%. If the steambonus* is taken into account, the process efficiency, based on exergy, is 91+

Figure 4 Grassmann diagram of the high-pressure LDPE process. Available work,lost work, and potential steam bonus streams are given as a percentage of the total

input.

* Steam bonus: If the steam generated by the process is used elsewhere on site or for, say,

heating purposes, the steam can be treated as a valuable bonus product. The heat liberated in

the reactor can be used to produce LP steam.

Chapter 11154

1.1 + 0.05= 92.2%. The main losses can be identified in the pie chart, whichis given in Fig. 5 and in Table 4.

As can be seen from the pie chart, Fig. 5, the Grassmann diagramin Fig. 4 and Table 4, the main losses can be attributed to the followingsections:

1. The reactor2. The HP cooler3. The HP flasher4. The Extrusion section

The loss in the reactor is mainly chemical in origin and can be attributedto the driving force of the chemical reaction, -DG/T. The losses in the cooler,the flash sections, and the extruder are solely physical exergy losses and can

Figure 5 Pie chart of main exergy losses in the HP LDPE process.

Table 4 Overview of Main Losses in the HP LDPE Process

Unit Exergy loss (%)Exergy loss(MJ/kgPE)

Exergy lossa

($/kgPE)

Reactor 53 2.284 0.0225

HP cooler 15 0.647 0.0064HP flash 13 0.560 0.0055LP flash 8 0.345 0.0034

Extruder 11 0.474 0.0047Total 100 4.31 0.0425

a Crude oil = 38.4 MJ/liter = 6105.6 MJ/bbl, 1 bbl = $15. A 25% efficiency to generate

electricity (exergy) from the crude oil is assumed (see Chapter 9).

Chemical Conversion 155

be attributed to large driving forces in temperature, chemical potential, andfriction, respectively. The physical exergy losses due to pressure drop in thetubular reactor are much smaller than the chemical exergy losses in thereactor. Low-pressure steam is produced by cooling the reactor, whichmeans the heat of reaction is put to good use. This results in a reduction ofthe physical losses in the reactor. Direct utilization of the Gibbs energy ofreaction to produce electricity in a fuel cell-type reactor is beyond thecurrent level of technology and is not considered feasible. The base case hastotal losses of 4.31 MJ/kg PE, which amounts to 2.82 � 10�3 bbl crude oil/kg PE, or US$0.0425 per kg PE (see Table 4).

5 PROCESS IMPROVEMENT OPTIONS

Losses could potentially be reduced by considering, for example, the fol-lowing options:

1. The losses in the HP flash can be reduced by using a turbine.2. Develop an alternative to extruders.

5.1 Lost Work Reduction by the Use of a Turbine

The theoretical* maximum amount of work (Wturbine) that can be obtainedfrom the turbine is given by the following expression:

Wturbine ¼_Ws

_m¼ �Dhs � gturbine

where _Ws, _m, and Dhs denote the shaft work, the mass flow rate, and theisentropic enthalpy change, respectively. If the efficiency, gturbine, is chosento be 0.75, and the enthalpy difference is calculated for the pressure dropfrom the reactor exit pressure (2200 bar) to 1000 bar,y the following turbineduty can be computed:

Wturbine ¼ 0:32MJ=kg PE

The savings, therefore, are 0.32 MJ/kg PE. The original loss was (see Table4) 0.56 MJ/kg PE for the HP flash, which means that 0.24 MJ/kg PE will still

* The figure calculated is theoretical, as turbines that can handle this pressure have not been

built yet.yAt lower pressures a two-phase mixture is obtained, which is not desirable for turbine blades.

Chapter 11156

be lost. A noteworthy point, however, is that turbines do not exist yet thatcan operate at these kind of pressures!

5.2 Alternative to the Extruder

The extruder is used since it mixes, melts, and degases the polymer.However, as said in the previous paragraph, from an exergetic point ofview, it is not an efficient apparatus, since it dissipates mechanical work intoheat by frictional forces. A possible alternative to the extruder couldtherefore be a separate degasser, static mixer, and gear pump to push thepolymer melt through the mixer and perforated plate (Fig. 6).

The extruder is substituted by a deep flash vessel (which operates at150 mbar), a gear pump, and a static mixer. The only exergy input is theenergy requirement of the pump and the compressor, which removes thegas. The pump only needs to increase the pressure of the polymer such thatit can pass through the static mixer and the granulating head (perforatedplate). This results in the following expression for the exergy input:

E _xin ¼ _m

gmechqDPstatic�mixer þ DPgranulating�head� �þ E _xcompressor

where _m is the mass flow rate of polymer passing through the mixer, Dmech

the mechanical efficiency of the gear pump (50%), and U the density of thepolymer. By computing the pressure drop in the static mixer and the pres-sure drop in the granulating head and adding this to the exergy requirementsof the compressor, it is possible to compute the exergy input of the alter-native scheme, and compare this with the regular extruder (Fig. 7).

As the graph suggests, it is beneficial to use the proposed setup. It is, ofcourse, unclear what the effect of the new setup will be on product quality,which stresses the use of laboratory experiments with the new setup. Theinitial exergy loss with the extruder was 0.47 MJ/kg PE (see Fig. 5 and Table

Figure 6 Alternative to the extruder.

Chemical Conversion 157

4). The estimated exergy loss with the new setup will now be between 0.6 �0.47 = 0.285 MJ/kg PE (for a diameter of 0.1 m) and 0.15 � 0.47 = 0.071MJ/kg PE (for a diameter greater than 0.4 m) depending on the diameter ofthe static mixer.

5.3 Process Improvement Options: Estimated Savings

The total initial losses were 4.31 MJ/kg (see Fig. 5 and Table 4). Theestimated savings per improvement option are as follows:

1. Turbine to address HP flash losses: 0.32 MJ/kg PE savings, whichgives a new loss of 0.24 MJ/kg compared to the original 0.56 MJ/kg PE. This translates into a savings of US$0.003 per kg PE.

2. Alternative to extruder: savings between 0.19 MJ/kg PE and 0.40

MJ/kg PE, which gives a loss between 0.07 MJ/kg PE and 0.28MJ/kg PE compared to 0.47 MJ/kg PE.

Option 1 is not yet technologically viable but option 2 is.

6 RESULTS OF THE GAS-PHASE POLYMERIZATIONPROCESS EXERGY ANALYSIS

The results of the exergy analysis of the gas-phase process are given below asa Grassmann diagram (see Fig. 8). The efficiency of the gas-phase process is91%. The main losses can be identified and are shown in the pie chart givenin Fig. 9 and in Table 5.

Figure 7 Scaled exergy input of the alternative extruder and regular extruderplotted against static mixer diameter.

Chapter 11158

The losses in the reactor are chemical exergy losses, whereas the coolerlosses can be attributed to physical exergy losses. Mixing constitutes phys-ical losses as do the losses in the extruder due to dissipation of mechanicalenergy to heat. The losses in the purge vessel (V3) are due to the fact that thegas is incinerated. The sum of all losses equals 4.73 MJ/kg PE, or 0.0465US$/kg PE.

Figure 9 Pie chart of main exergy losses in the gas-phase process.

Figure 8 Grassmann diagram of the gas-phase process. Exergy and lost workstreams are shown as a percentage of the total input.

Chemical Conversion 159

7 PROCESS IMPROVEMENT OPTIONS

Losses in the gas-phase polymerization process can be reduced, for example,by taking the following steps:

1. Coupling reactions to reduce the chemical exergy loss in thereactor.

2. Reuse the gas that leaves the purge vessel instead of burning it.3. Use the heat discarded by cooler H1 to heat the polymer in the

extruder after upgrading with a heat pump.4. Preheat the polymer to its melting point, thus reducing the exergy

consumption of the extruder.5. Develop an alternative to extruders.

Note that for the gas-phase polymerization process, the PE enters theextruder in solid form between 70–80jC, which is approximately the upperlimit for solids handling. For safe and easy handling of solid PE, thehandling temperature is usually chosen 40jC below the melting point, whichresults in 85jC. At higher temperatures, the morphology of PE becomessuch that handling is difficult (sticky solids).

7.1 Coupling Reactions and Chemical Heat Pump System

The exergy loss in the reactor is formally defined as

E _xloss ¼ _mðExin�ExoutÞ ð3ÞSince the chemical exergies in this case are much larger than the physicalexergies, the exergy loss is dominated by the difference in chemical exergy(=�DrG

0). The reaction is accompanied by changes in entropy and enthalpy

Table 5 Overview of Main Losses in the Gas-Phase PE Process

Unit

Exergy

loss (%)

Exergy loss

(MJ/kgPE)

Exergy lossa

($/kgPE)

Reactor 36 1.703 0.0166Cooler H1 15 0.710 0.0069Efficiency lossC1 4 0.189 0.0017

Mixing losses 10 0.473 0.0046Extruder 17 0.804 0.0076Surge vesselV3 20 0.946 0.0092

Total 100 4.73 0.0465

a Crude oil = 38.4 MJ/liter = 6105.6 MJ/bbl, 1 bbl = $15. A 25% efficiency to generate

electricity (exergy) from the crude oil is assumed (see Chapter 9).

Chapter 11160

(heat of reaction). These losses can, in theory, be reduced by building thereactor in a way that it resembles a fuel cell, since fuel cells have the capacityto transform in the reversible limit the full Gibbs energy change intoelectricity. For polymer systems, this is unfortunately not a viable option.The only option that remains is to somehow use the heat liberated duringreaction. The heat of reaction, which is currently not being utilized, couldpotentially be harnessed if a chemical heat pump were used. A chemical heatpump is simply a system that uses a chemical reaction to absorb heat at acertain temperature and uses the reverse reaction at a different temperatureto release this heat. A list of proven chemical heat pump systems is given inKyaw et al. [4]. Unfortunately, none of these systems is viable in a fluidizedbed reactor since additional reactions in the reactor, known as direct cou-pling, may reduce product quality, poison the catalyst, or necessitate ex-ergetically costly separation steps to remove PE from the species used in thechemical heat pump systems. Indirect coupling would require a heatexchanger in the reactor, which would change the hydrodynamics in thereactor, thus potentially affecting conversion.

At this stage, therefore, chemical heat pump systems are not consid-ered viable for the PE gas-phase polymerization reactor [3].

7.2 Exergy Loss Reduction by Recovering Butyleneand Ethylene from Purge Gas

This option is relatively simple to implement and would save a maximum of0.946 MJ/kg PE if reused completely, which is a theoretical upper bound.The exergy of this purge stream is dominated by the chemical exergies of theconstituents. If all butylene is recovered using a cooling cycle, the exergysavings will be 0.416 MJ/kg PE, and the losses would have been reduced to0.530 MJ/kg, as the ethylene is not recovered. If the ethylene is recovered aswell, the savings will be 0.946 MJ/kg PE.

Alternately, the purge stream can be sent to a powerplant where (at 25%efficiency) electricity is produced, resulting in a loss reduction of 0.25 � 0.946=0.2365MJ/kg.Hybrid options are also possible, where part is sent to a pow-erplant to generate the electricity necessary to power the cooling of the reactor.

7.3 Heat Pump and Preheating of Polymer

A potentially viable improvement to increase the exergetic efficiency is tofeed solid PE to the extruder, and to recycle a part of the molten PE, whichis then heated to a much higher temperature by utilizing the waste heat ofthe process upgraded by a heat pump system (see Chapter 5 for details). Thehot molten PE quickly melts the solid feed upon entrance in the extruder,thus resulting in lower exergy requirements (Fig. 10). The theoretical power

Chemical Conversion 161

consumption (per unit mass PE passing through the extruder) of an extruderis given by the following equation, since the extruder heats the polymer andtransports it against a pressure gradient:

Wextruder ¼Z T2

T1

CpdTþ DP

q

Now, with the recycle option, the total mass flow rate through theextruder will increase and, therefore, the power consumption based on PEproduced (i.e., leaving the recycle loop) will increase. The following graph(Fig. 11) shows the exergy savings of the extruder and the exergy input toheat the PE in the heat exchanger as a function of the final temperature ofthe liquid PE after passing through the heat exchanger (Tinlet). In this graph,the mass flow rate of PE in the extruder has doubled, since an equal amountof PE leaves the recycle loop and stays inside it.

Since waste heat (H1) is available, this heat can be used to be upgradedwith a heat pump. If compressor and pump efficiencies of 75% are assumed,and a simple two-stage vapor-compression heat pump is used, the totalsavings (extruder exergy savings and waste heat savings) can be calculated,as well as the exergy input for the heat pumps (see Fig. 12). As at higher inlettemperature,* the total savings are larger than real exergy input for theextruder, so it is useful to consider this option.

Figure 10 Extruder using recycled and upgraded heat.

* It is undesirable to elevate the temperature of PE far above 300jC due to product quality

concerns. The maximal gains are therefore 0.4 - 0.2 = 0.2 MJ/kg PE.

Chapter 11162

7.4 An Alternative to the Extruder

If the set-up shown in Fig. 13 is chosen instead of an extruder, it can becalculated that exergetic gains are obtained as shown earlier.

For the gas-phase process, in which solid PE is fed into the extruder,the extruder can be substituted by a kneader (to melt the polymer bydissipation of mechanical energy), a gear pump, a static mixer, and a gra-nulator. By using a enthalpy-temperature correlation for PE, the kneaderduty necessary to melt the polymer can be calculated. The calculation of thegear pump duty was shown earlier (Section 11.5.3). The graph in Fig. 14shows the (scaled) exergy requirements of the alternative extruder withrespect to the original extruder.

Figure 11 Exergy savings and input for recycle option (see Fig. 13).

Figure 12 Total exergy savings (extruder and H1) and exergy input.

Chemical Conversion 163

From an efficiency point of view, the new setup is advantageous. Asthe pressure drop across the static mixer is approximately 25 MPa (fordiameter 0.5 m; see Fig. 15), the proposed setup is feasible,* as gear pumpsare known to deliver pressure of 35–40 MPa. Another advantage of theproposed setup is that the polymer can be degassed further than is possiblein the extruder. The present extruder loses 0.17 � 4.73 = 0.8041 MJ/kg PE.The savings will be between (1 � 0.44) � 0.17 � 4.73 = 0.45 MJ/kg PE and(1 � 0.74) � 0.17 � 4.73 = 0.21 MJ/kg PE. The values of 0.44 and 0.74 canbe determined graphically from Fig. 15.

7.5 Process Improvement Options: Estimated Savings

The original losses were 4.73 MJ/kg PE (see Fig. 9 and Table 5). Theestimated savings per improvement option are as follows:

1. Recover gases from purge stream: 0.946 MJ/kg PE, which reducesthe losses to 0 MJ/kg PE. Recovery costs in terms of exergy areminimal and have not been shown.

2. Use the gases in the purge stream in a powerplant: 0.24 MJ/kg PE,which reduces the loss to 0.71 MJ/kg PE.

3. Heat pump and preheating of polymer in the extruder: 0.2 MJ/kg

PE, which reduces the losses from the original 0.8 MJ/kg PE to 0.6MJ/kg PE.

4. Alternative to extruder: between 0.21 MJ/kg PE and 0.45 MJ/kg

PE, which reduces the losses from 0.8 MJ/kg PE to between 0.59MJ/kg PE and 0.35 MJ/kg PE.

All these options are technologically viable.

* The change from extruder to gear pump/static mixer could potentially increase the gel count.

As LDPE and LLDPE primarily find their uses in foils, laboratory scale tests are recom-

mended to assess the impact of the proposed setup on the gel count. Extruders usually de-

crease the gel count by kneading the polymer. It is unclear whether the proposed setup can

accomplish the same.

Figure 13 An alternative to the extruder.

Chapter 11164

8 CONCLUDING REMARKS

The objective of this chapter was to show how exergy analysis can helppinpoint steps where lost work is produced or, equivalently, exergy lossesare greatest in chemical processes. Since the analysis was based on a flowsheet of a process, exergy analysis can be used as a tool to improve the ef-ficiency of processes when they are still in the design stage. This can helpmove chemical processes closer to the ideal of a sustainable chemical pro-cess. The process improvement options are by no means definitive, and astechnology evolves better options will become available. The cases presented

Figure 14 Exergy requirement of alternative and existing extruder as a function ofthe static mixer diameter.

Figure 15 Pressure drop across static mixer for different diameters.

Chemical Conversion 165

in this chapter do, however, indicate how good chemical engineering coupledwith exergy analysis can make a difference in making processes moreefficient and durable.

REFERENCES

1. Encyclopedia of Polymer Science and Engineering; editor-in-chief Kroschwitz,J.I., John Wiley: New York, 1990.

2. Szargut, J.; Morris, D.R.; Steward, F.R. Exergy Analysis of Thermal, Chemicaland Metallurgical Processes; Hemisphere Publishing Corporation: New York,1988.

3. Sankaranarayanan, K., M. Sc. Thesis. Delft University of Technology: Delft,The Netherlands, 1997.

4. Kyaw, K.; Matsuda, H.; Hasatani, M.J. Chem. Eng. Japan 1996, 29 (1), 119.

5. Encyclopedia of Polymer Science and Engineering; editor-in-chief, Kroschwitz,J.I., John Wiley: New York, 1990.

Chapter 11166

12A Note on Life Cycle Analysis

In this chapter we briefly touch on a tool called life cycle analysis and discussits usefulness.

1 INTRODUCTION

In the previous chapters, thermodynamic analysis is used to improve pro-cesses. However, as pointed out in Chapter 9 (Energy Conversion), the ex-ergy analysis did not make any distinction between the combustion of coaland natural gas and, as a result, could notmake any statements regarding tox-icity or environmental impact of the two fuels. A technique that can do this islife cycle analysis (LCA). What exactly is life cycle analysis? In ISO14040 [1],life cycle analysis* (or life cycle assessment) is defined as ‘‘the compilationand evaluation of the inputs, outputs and potential environmental impactsof a product throughout its life cycle.’’

Increased environmental awareness has led to the emergence of the con-cept to conduct a detailed examination of the life cycle of a product or a pro-cess. In the late 1960s and early 1970s, global modeling studies and energyaudits were conducted to evaluate the costs of resources and the environmen-tal implications of mankind’s behavior. The LCAs were a natural extensionof this and are useful in assessing the environmental impact of various prod-ucts. They are also slated to be used in so-called eco-labels that allow theconsumer to discern between various products. LCA is a potentially powerfultool that can be used in many instances. It can, for example, be used to (1)analyze products and processes and improve these, (2) to assist in formulating(environmental) legislation or steer public policy [2], and so forth. In using

167

*Recently, terms such as life cycle inventory (LCI), cradle-to-grave-analysis, eco-balancing, and

material flow analysis have come into use.

the tool, some care must be taken. Like most tools, it must be used correctly.A tendency to use LCAs to ‘‘prove’’ the superiority of one product over an-other has cast a shadow of disrepute over the concept in some areas [3].

Thus, LCA is a tool to evaluate and analyze the environmental burdenof a product throughout all stages of its life. Thermodynamic analysis, onthe other hand, is not restricted to a product, but is equally well applied inthe analysis of processes. A product and a process are separate entities, butthey are related since the purpose of a process is tomanufacture a product. Be-cause of this, thermodynamic analysis can easily be used for a product (e.g.,lost work per unit weight product, as in the polyethylene case study, Chap-ter 11).

The environmental burden covers all impacts on the environment andincludes extraction of raw materials, emission of hazardous and toxic ma-terials, land use, and disposal. In certain cases, the analysis only takes intoaccount the burden up to the ‘‘gate’’ of the producing facility, and in othercases, the analysis takes into account the actual disposal of the product. Inthe former case, the analysis is termed a ‘‘cradle-to-gate’’ analysis, while thelatter is referred to as a ‘‘cradle-to-grave’’ analysis.

Thus LCAs are useful in (1) quantifying environmental impact andcomparing various process routes for the same product, (2) comparing im-provement options for a given product, (3) designing new products, and (4)choosing between comparable products. In Section 2 we outline the generalmethodology of LCA, and we conclude with Section 3.

2 LIFE CYCLE ANALYSIS METHODOLOGY

Broadly speaking, a life cycle analysis consists of the following steps:

1. Goal and scope definition2. Inventory analysis3. Impact assessment4. Interpretation and action

2.1 Goal and Scope

An LCA typically starts by defining the goal and scope of the study. Thegoal and scope definitions are important since they define the level of detailin the study. The exact question to be answered using the LCA method isformulated (e.g., for product X, two process pathways exist. Which pathwayhas the least environmental burden?). Too often, this step is given too littletime, and the LCA is launched and completed. However, without a proper

Chapter 12168

goal definition, it is impossible to say whether the study was successful [4]!From [5] we can obtain the following definitions.

The goal definition element of an LCA identifies the purpose for thestudy and its intended application(s). This step will present reasons whythe study is being conducted and how the results will be used. Scoping

defines the boundaries, assumptions, and limitations of a particularLCA. It defines what activities and impacts are included or excluded andwhy. . .. Scoping should be attempted before any LCA is conducted toensure that:

� The breadth and depth of analysis are compatible with and

sufficient to address the goal of the LCA.� All boundaries, methodologies, data categories, and assump-

tions are clearly stated, comprehensible, and visible.

The goal-and-scope definition process is an integral part of any LCAstudy. At the outset of an LCA, before any data are collected, key de-cisions must be made regarding the scope and boundaries of the systembeing studied. These decisions are mainly determined by the goal, i.e.,

the defined reasons for conducting the study, its intended applications,and the target audience.

The scope definition is similar to the definition of the control volume in thethermodynamic analysis or the battery limits in process design, and for theLCA in terms of space and time (e.g., we follow the use of product X inthe process from the raw materials to the time it is disposed by the con-sumer. Throughout the lifetime of the product, we analyze the environmen-tal burden). The reasons for the study are also clearly defined (e.g., is thestudy necessary to make a decision about a process?), as well as an answermust be given as to who is performing the study and for whom. Consider thefollowing hypothetical example:

The goal of this LCA study is to examine the environmental burden ofusing polyethylene film (made with the high-pressure tubular process) forfood packaging. The results will be used to improve the environmental

performance of the production process by changing, where possible,process parameters. This LCA will not compare the polyethylene filmmade by the high-pressure tubular process with that made with the high-

pressure autoclave process.The LCA will be performed by an in-house team of engineers and

has been commissioned by Food Packaging Inc., which uses the poly-ethylene film. An overseer fromFood Packaging Inc. has been assigned to

review the study.The LCA is performed for Food Packaging Inc., which is based in

New Jersey. The data for the study will come from the plant, which is

based in New Jersey. The total size of the study is 10 person months, and

A Note on Life Cycle Analysis 169

the bulk of the time will be spend on gathering the data necessary for thestudy andwill not include the ultimate disposal of the food packaging film(cradle-to-gate).

It is clear from this hypothetical example what is going to be studied, bywhomand who commissioned it.

It is important to note that the LCA is a tool and cannot provide anall-encompassing assessment. One of the reasons is that industrial processesare interconnected globally so that complete consideration of all these inter-dependencies is practically impossible. Also, the results of an LCA are ap-proximations and simplifications of cumulative burdens to the environmentand of resources used. Therefore, the LCA process does not directlymeasure actual environmental impact, predict effects, or represent causallinkages with specific effects. As a result, to meet the needs of the studyusers, it may be necessary to supplement the LCA with other tools ormethods to provide a basis for decision-making. These tools include riskassessment, site-specific environmental assessment, etc. As a part of thescoping process, it is useful to identify where and how these other tools willbe used to augment the findings of the LCA [5].

A noteworthy point is that in certain cases it is convenient to speak interms of function. For example, the main function of the plastic film is tokeep the food fresh for a specific duration of time. In cases that a compara-tive study is commissioned, and alternatives are required, the functiondefinition is important to clearly state what the product is meant to do, soalternatives can be sought.

2.2 Inventory Analysis

Probably the most important step in the LCA is the inventory analysis,which carefully documents the (raw) materials necessary for the product, theemissions, required energy input and environmental burden at disposal byeither recycle, disposal, etc. Here it is very useful to clearly mark the systemboundaries. ISO 14040 [1] defines inventory analysis as follows:

Inventory analysis involves data collection and calculation procedures

to quantify relevant inputs and outputs of a product system. These in-puts and outputs may include the use of resources and releases to air,water, and land associated with the system. . . . These data also con-stitute the input to the life-cycle impact assessment.

Let us take the polyethylene (PE) mentioned in the goal as an example. Poly-ethylene is produced from ethylene, as we saw in Chapter 11. The ethylene,on the other hand, comes from a refinery or chemical plant, and the ultimatesource of ethylene is, therefore, crude oil or another fossil fuel source. Ener-gy is required for the process, and thus electricity is generated. There are

Chapter 12170

emissions at the various stages. The final PE is then used to package food.The control volume does not take into account the disposal of the plasticfilm, since the goal stated that this was a cradle-to-gate analysis.

The key concept of inventory analysis is that all in- and outflows ofmatter are carefully documented. This inventory is therefore cumulative (seeFig. 1). For example, an inventory of the polyethylene production can be con-structed from plant data (note the compounds and figures are hypothetical inTable 1).

For the ethylene, similar data could be constructed from either anaverage of ethylene producers in this geography or on-site naphtha crackers.In certain cases, databases exist for certain commonly used compounds. Inother cases, data are unavailable and estimates have to be made. In case ofplants that produce more than one product, the total emissions are allocatedproportionally to their sales.

2.3 Impact Assessment

Once a complete inventory has been generated for the product, the impactcan be assessed. According to ISO 14040, various classes of impact exist.These classes can either coincide with known groups such as acidification,

Figure 1 Example of cumulative inventory.

A Note on Life Cycle Analysis 171

global warming, and resource depletion or be specifically defined to be in linewith the goal [6]. Various characterization methods exist for these classes. Forexample, human toxicity potential (HTP) is a possible measure for humantoxicity, whereas acidification potential is a useful measure for acidification.Thesemeasures usually allow the transformation of the results into equivalentamounts of a certain compound and allow for the transformation of the totalinventory in an environmental profile. Once this environmental profile iscomplete, the results are normalized with respect to reference information fora certain community at a certain time.Weighting, which is an optional step inthe impact assessment, can be used to highlight certain categories by assigningweight factors.

2.4 Interpretation and Action

This step is difficult since the results have to be interpreted, and the inter-pretation will be subjective. For example, what is more important—the en-vironmental burden of acidification or global warming? To answer thesequestions, the goal and scope definition must have been given proper care.

3 CONCLUDING REMARKS

In this chapter, we gave a brief outline of LCA. It is beyond the scope of thisbook to give detailed instructions on how to perform every step, but we hopethat the mechanics of the procedure are clear. For more details regardingLCA, we refer to the publications of the Society of Environmental Toxicol-ogy and Chemistry and the International Standards Organization. It maybe useful to analyze processes using a combination of exergy analysis and

Table 1 Example of Inventory (Hypothetical) ofPE Plant

Polyethylene productionSource of data: PE plantDate: Jan. 1, 2002Geography: North America

Economic input: EthyleneEconomic output: PEEmissions:

CO2 0.5 kg/kg PEEthylene 12 mg/kg PE

Chapter 12172

life cycle analysis, since both methods have the potential to quantify theenvironmental burden. In this case, it would be preferable to use a cumu-lative exergy analysis to obtain estimates of the exergy required to manu-facture a certain product (and of course also the lost work), and use the lifecycle analysis methodology to obtain estimates for green house emisions, forinstance.

REFERENCES

1. Environmental Management—Life-Cycle Assessment—Principles and Frame-

work. ISO 14040, International Standards Organization, Oct. 1998.2. Consoli, F.J.; Davis, G.A.; Fava, J.A.; Warren, J.L. Public Policy Applications of

Life-Cycle Assessment; Allen, D.T., Ed.; Society of Environmental Toxicologyand Chemistry (SETAC), 1997.

3. http://www.gdrc.org/uem/waste/life-cycle.html, source World Resource Foun-dation.

4. Weitz, K.; Sharma, A.; Vigon, B.; Price, E.; Norris, G.; Eagan, P.; Owens, W.;

Veroutis, A. Streamlined Life-Cycle Assessment: A Final Report from the SETACNorth America, Streamlined LCA Workgroup; Todd, J.A. Curran, M.A., Eds.;Society of Environmental Toxicology and Chemistry (SETAC), 1999.

5. Fava, J.; Denison, R.; Jones, B.; Curran, M.A.; Vigon, B.; Selke, S.; Barnum, J.;Eds.; A Technical Framework for Life-Cycle Assessment; Society of Environ-mental Toxicology and Chemistry (SETAC): Pensacola, FL, 1991.

6. Barnthouse, L.; Fava, J.; Humphreys, K.; Hunt, R.; Laibson, L.; Noesen, S.; Nor-

ris, G.; Owens, J.; Todd, J.; Vigon, B.; Weitz, K.; Young, J., Eds.; Evolution anddevelopment of the conceptual framework and methodology of life-cycle impact as-sessment an addendum to Life-Cycle Impact Assessment: The State-of-the-Art. 2nd

Ed. Society of Environmental Toxicology and Chemistry (SETAC), 1997.

A Note on Life Cycle Analysis 173

13Sustainable Development

Sustainability is what it is all about.

—Brundtland Report,World Commission on Environment and Development (1987)

So far all our contributions and attention have been focused on thethermodynamic efficiency of processes. Theory provided us with thermody-namic tools with which we could establish the difference between the realand the minimum amounts of work required and identify this difference aslost work. We could also show the way to keep these losses to a minimumgiven the various constraints to the process: thermodynamic optimization.But operating processes efficiently is not enough; an emerging requirement isthat our technology be also sustainable. Most people have an intuitive no-tion of what sustainability is, but our examples will show that there is a needfor substantiation and, if possible, for quantification of this concept.Biology shows us that nature most probably provides us with what is, inour opinion, an elementary and perfect example of sustainability. Similarly,a simple economic analysis points to the essentials of what is a sustainableeconomy and what this implies for operating our industry. One conclusionseems to be that technology needs to learn some essential lessons from na-ture. Industry, mainly based on nonrenewable resources, should be trans-formed into one based on renewable resources. In more general terms, asociety, driven by material energy sources with, as a consequence, materialemissions, should be transformed into one driven by immaterial sources ofenergy such as radiation, wind, geothermal energy, and so on, resulting innonmaterial emissions.

Solar energy seems to be abundant compared to the energy our societyrequires and is therefore an obvious candidate for energy supply. But a closeranalysis shows that even here there might be, for the moment, significantlimitations.

175

1 SUSTAINABLE DEVELOPMENT

After one of our studies on the efficiency of industrial processes had beencompleted, the client contacted us again some time later and asked us for adefinition of sustainability. More specifically, his industry was probably notsustainable but if it was not, was it close or remote? The client suspected thatthis was a question with a high thermodynamic content and had thereforecontacted us again: ‘‘Your discipline should be able to tell us more aboutit.’’ Now, some years later, our conclusion is that his intuition was partlyright: Thermodynamics is of great help in structuring the concept of sus-tainability and in giving it a sound basis for quantification. But strictlyspeaking, it is not essential for understanding and defining it, as we willillustrate in the following.

According to the China Daily of November 3, 2001, the term ‘‘sus-tainable development’’ was catapulted into the consciousness of world lead-ers at the United Nations Conference on Environment and Development inRio de Janeiro in 1992. At its core was an understanding that development,namely poverty eradication, is integrally tied to keeping the world’s naturalresources and ecosystems free from pollution and degradation. Agenda 21,called by some the blueprint for sustainable development, is a collection ofcommitments by governments on climate change, biological diversity, andforestry principles. In 2002 South Africa hosted the first World Summit onsustainable development to assess and evaluate progress made in the 10years since the Rio Declaration.

Of course, the term ‘‘sustainable development’’ was first launched withsuccess in a United Nations report called ‘‘Our Common Future’’ [1], betterknown as ‘‘The Brundtland Report’’ after the chairperson of the commissionthat produced it. In this report, sustainable development is defined as a socialdevelopment required to satisfy the needs of present generations withoutputting at risk the needs of future generations.

Trilemma: Three Major Problems Threatening World Survival [2] pointsout that amid the explosive rate at which the world population is increasing,from 5 billion people in 1995 to an estimated 10 billion people in 2040 [3],mankind is faced with a triad of serious problems: an unprecedentedeconomic growth; consumption of energy and resources; and all this in tryingfor conservation of the environment. In the authors’ words, the world isfacing a formidable trilemma that can only be obviated by what they call asustainable development. Such a development can be accomplished by aserious multidisciplinary effort in which science, technology, sociology, andeconomy seem as yet to be the most prominent disciplines.*

Harmsen [4] points out that there are several views with which one canlook at sustainable development. One view is the theocratic view, prominent

Chapter 13176

in Judeo-Christian religion in which the Creator stands central and needs tobe honored and served by Man. Nature is trusted to Man, who should takecare of it, while Technology should help him and simplify his task. Manassumes this responsibility much as a steward of property and capital does.This is the same role as the one many responsible company directors play:The interest of the company should be served and is central in one’s per-formance and behavior toward the company. This view is to some extentexpressed in a moving way by the text on the statue of the Japanese-Amer-ican environmentalist Yasui Minoru in Denver’s Sakura Center: ‘‘We are allput on this earth to leave it a better place for our having been here.’’

In the ecological view Nature is central. By Nature is meant all livingsystems, the climate, and natural resources. Human actions and activityshould preserve Nature’s integrity, stability, and beauty. Technology shouldbe embedded in Nature. Exchange of materials should take place in closedcycles, whose conditions are so severe that it seems that onlymaterials of plantorigin can fulfill it. This view can be recognized in Yoda’s nearly desperatewords when he states in Trilemma that ‘‘Nature has lost its ability to cleanseitself.’’

In the anthropological viewMan is central, which is best illustrated withthe popularized definition of sustainable development from the earlier citedBrundtland Report [1]: ‘‘fulfilling the needs of the present generationswithout sacrificing the needs of future generations.’’A very ‘‘down-to-earth’’definition is given by Okkerse and van Bekkum [3] in their chapter ‘‘Towardsa plant-based economy’’: ‘‘Feed double the number of people, provide themwith energy and materials, let them live according to the requirements of adeveloped society and do not pollute the earth nor change the climate.’’

It is interesting to read what ‘‘captains of industry,’’ such as thechairmen of prominent multinational companies, have to say about sustain-able development. Sir Marc Moody-Stuart, former chairman of the Com-mittee of Managing Directors of the Royal Dutch/Shell Group ofCompanies, stated in 1999 in Newsweek [5] what sustainable developmentmeant for his company: ‘‘balancing our own legitimate commercial interestswith the wider need to protect and enhance the environment and contributeto social progress and stability.’’

*Suppose a scientist, say a physical chemist, discovers a new principle by which solar energy can

be converted into electricity. The engineer is required to make this principle work in practice.

The economist will be needed to assess the economic feasibility, which should include

ecological aspects. But even then the sociologist may be needed to explain why people don’t

buy it. If the innovation serves a global interest, a multidisciplinary effort with participants

also skilled in communicating the essence of their discipline to each other will enhance the

successful introduction and acceptance of the innovation.

Sustainable Development 177

Morris Tabaksblatt, as former chairman of Unilever, emphasized in aspeech [6] that within his company ‘‘No business or policy decision can betaken before it has been tested on its impact on sustainable development.’’

We conclude this brief review with what has been perhaps the mostrigorous and strict definition of sustainable development so far. It has beengiven by Dr. Angela Merkel, a physicist from Leipzig University, while shewas GermanMinister of the Environment, Nature Conservation andNuclearSafety. Discussing ‘‘The role of science in sustainable development,’’ shestates inScience [7], ‘‘Sustainable development seeks to reconcile environmen-tal protection and development; it means nothing more than using resourcesno faster than they can regenerate themselves, and releasing pollutants to nogreater extent than natural resources can assimilate them.’’ This definition is,in our opinion, of dramatic dimension and consequence while also nonreal-istic, because of the impossibility to effectively adopt it in the short term.When prestigious scientists as the American and Japanese economists RobertAyres [8], and Sawa Takamitsu [9] appeared to use the termsmetabolic societyand industrial metabolism, it seemed to us wise to turn to some prominentbooks on biochemistry [10] and bioenergetics [11].

2 NATURE AS AN EXAMPLE OF SUSTAINABILITY

Industry and our industrial society lean heavily on material resources, rawmaterials, and energy or fuels. Most of these resources have a limited abun-dance; we consume them and do so without regeneration. From this supplybasis we produce electricity, mechanical energy, heat, chemicals, and otherspecified materials, sometimes of great purity or complexity. Nature, inparticular or more specifically living or animate systems, does the same butin a remarkably different way that appears to send us a clue for what weshould understand by sustainability. A closer analysis shows that man andanimals do not seem to be essential for the maintenance of sustained life, butplants and micro-organisms are. Man and animals are ultimately dependenton plants. Plants and micro-organisms are essential for life and cannot livewithout each other. They live on air, water, minerals and sunlight,* andbased on these they make complex compounds necessary to sustain life.

* In a wonderful article [21] the late Stephen Jay Gould discusses that life based on solar energy

and photosynthesis may be the exception rather than the rule. Equally he disputes that the

bulk of life’s biomass should reside in the wood of trees in our forests and argues that the mass

of subterranean living material as that of bacteria is comparable to that at the surface and is

possibly in excess of it.

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Energy can be converted into chemical, mechanical, and electrical energyand work for transportation and concentration of matter and for trans-porting signals through the nerve system. At the synthesis side, photosyn-thesis is the start of building a complex material system. At the respirationside, oxygen breaks down complex molecules to transfer chemical energy toall other forms of energy to sustain life. Ultimately, all originally absorbedsolar energy will be transformed into heat that is radiated into the universe.Figure 1 clearly illustrates what we have just described. It pictures in aprimitive and limited simplification how matter is cycled in a closed systemof the biosphere and is neither absorbed nor emitted. The biosphere acts asan open system, however, for energy, taking in solar energy and emittingthis energy in the degraded form of heat into the universe. Solar energyabsorbed is, in contrast to fossil fuel, an immaterial source of energy, andafter this has permeated through the biosphere, it is emitted as an imma-terial form of energy: heat. Meanwhile the biosphere extracts this solarenergy partly from its useful part for conversion into many forms of energy.The essence is that matter is recycled in this ‘‘cycle of life,’’ without net ma-terial intake or output, partly stripping incident solar energy from its avail-able work. Only a very small fraction (<1%) of the incident solar energy isutilized in this way. The major part of the incident energy is directly emittedas heat. Ultimately, the minor part will also be emitted as heat after it hasbeen degraded via the living systems. So there is a strictly unidirectional flow

Figure 1 The metabolic society.

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of energy from the sun to the earth and into the universe. Only a very smallpart of this flow will be delayed via a detour through living systems.

As for the micro-organisms, they appear to be vital in the degradationprocess. Nature does not seem to know waste, as some micro-organism willalways take care of it and lead it back to carbon dioxide and water or otherbuilding stones for the more complex molecules of life. Micro-organisms areby far the most abundant form of life; in fact, nearly all life is made up ofthem. On one hand, they are able to fixate carbon dioxide and form oxygenin the process of synthesis; on the other hand, they are elementary in thedegradation of living matter to the elementary building blocks.

The general conclusion of this analysis seems to be that the biologicaldefinition of sustainability is that use should be made of an immaterial per-manent source of energy, like solar energy or the heat of the inner earth, andthat matter should move in closed cycles.

3 A SUSTAINABLE ECONOMIC SYSTEM

Another interesting approach leads to the same definition of sustainability—it comes from economics. In the view of classical economics there is an‘‘equilibrium’’ among production, consumption, and capital (Fig. 2). Nec-essarily this equilibrium has a dynamic nature, much as the equilibrium inthermodynamics where on a macroscopic scale there may be ‘‘rest’’ butwhere on a microscopic or rather molecular scale there is ‘‘unrest.’’ An ec-onomic system, however, much like thermodynamic systems, interacts withits environment. The first and second laws govern the evolution of a systemin its environment toward equilibrium in thermodynamics and can accountfor the nonequilibrium dynamic state, as in living systems, and its steady

Figure 2 Classical economics.

Chapter 13180

state. An economic system, much like a thermodynamic system, also has anenvironment, and, as has become clear in recent times, this environment is ofglobal dimensions. The economic system is driven by a finite amount ofresources, and this stock is not infinite. Similarly, the economic system hasits byproducts—waste—and the environment has no infinite absorptivecapacity for this waste. So supply of resources and absorption of wastecannot be taken for granted, and the classical picture of an economic sys-tem, in Fig. 2, has to be extended as in Fig. 3. This picture is characteristicfor so-called environmental economics or, even better, ecological economics.These economists thus recognize features of the economic system that aremost common in thermodynamics where the main laws express the prevail-ing interaction between the system under consideration and its environment.The extent to which matter and energy are exchanged dominates thisrepresentation. An economic system, therefore, much resembles a dynamicnonequilibrium system as discussed in the last section, much like living sys-tems. Food sustains the living system; material resources and energy sustainthe economic system. It is for this reason that some economists [12,13] statethat the production factors labor and capital are outdated and archaicconcepts and that the real production factors are matter and energy, or evenbetter exergy and information, serving both Man, Machine, and Nature.

Figure 3 emphasizes the finite nature and strong irreversibility of aneconomic system. The stock of energy and resources will eventually run outand so will the absorptive capacity of the environment for waste. An obvi-ous extension of Fig. 3, therefore, is the one represented by Fig. 4. Just likein nature, waste has to be recycled. In nature there is no real waste. Everyform of waste is a resource for a living system. This living system is verysmall and called a microbe. Microbes make sure that all matter recycles innature. Man needs to assume this humble but valuable and important roleof microbes in the economic system and make sure that the material cyclesget closed. Therefore, energy (or rather work) is required. But obviously this

Figure 3 Environmental economics.

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work should not be supplied from a nonrenewable source, like fossil fuels,but rather from a renewable source like the sun. Figure 4 therefore seems tobe characteristic for a sustainable economic system and corresponds re-markably with the definition of sustainability from biological systems: Anonequilibrium dynamic system is sustained through the cycling of matter inthe system and its environment, driven by the supply of an immaterial, re-newable energy source. For the definition of what should be understood bya (non-)renewable source, we refer to Lems et al. [14] and Section 6 here.

4 TOWARD A SOLAR-FUELED SOCIETY: ATHERMODYNAMIC PERSPECTIVE

If we adopt the model for sustainability as we have developed in theprevious two sections, then one obvious necessity is to transform a mainlyfossil-fueled society into a society fueled by a more sustainable fuel such assolar energy. Solar energy is abundant and ‘‘renewable’’ on a time scale ofmillions of years. Its availability, estimated at 2.8 � 106 ExaJoules/annum(EJ/a =1018 J/a) exceeds by far the needs of our society, 350 EJ/a even in2040 (Table 1). In recent publications of Shell International [15], the world’senergy needs are estimated to be a factor 2.5–3 times larger in the year 2050than in the year 2000. Not all of the 2.8 � 106 EJ/a is accessible; estimatesare that ‘‘only’’ 300–3000 EJ/a or 0.01–0.1% can be captured.

Fossil fuel, like oil, coal, and gas, which takes care of more than 90%of industry’s energy needs, is not renewable on this time scale at least if we

Figure 4 Sustainable economic system.

Chapter 13182

adhere to the definition that a fuel is not renewable when its consumptionrate exceeds its production rate. With fossil fuel so prominent in our in-dustrial society, let us make a thermodynamic analysis of a fossil-fueledpowerstation. Our choice of fuel is natural gas, for reasons of simplicitytaken as pure methane. Natural gas has been called by some the fuel of the21st century because of its abundance, relative purity, and low carbon di-oxide production per unit of electricity. Figure 5 depicts the fate of the workavailable in natural gas, its exergy, from source to sink (i.e., all the way fromthe gas reservoir to the environment into which its emissions of heat andcombustion gases are released). The production of natural gas requiresexergy and so does its transportation to the powerstation. The exergy ofmethane is about 831 kJ/mole, so strictly speaking less work is available forthe powerstation due to the incurred exergy cost of production and trans-portation. Our reference should be natural gas as it is present and at rest in

Table 1 Situation Analysis 1995 and Prognosis for 2040

Critical global data 1995 2040

Population 5 � 109 10 � 109

Energy consumption 350 EJ 900 EJ

Energy consumption/cap 2200 W 3000 WAgricultural land 3.4 � 109 ha 2.8 � 109 haOrganic materials 300 � 106 ha 1000 � 106 ha

Source: Ref. [3].

Figure 5 The fate of work from natural gas.

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our environment. Nevertheless, for the discussion to follow and for theobservations to be made, our starting point will be methane, at P0 and T0, atthe powerstation. On our way to electricity the first loss incurred is that ofthe spontaneous combustion of methane. From earlier chapters we knowthat close to 30% of methane’s exergy is lost in this process, due to thereaction velocity and affinity, in other words the strictly irreversible natureof this spontaneous process (see Chapter 4). Then the powerstation trans-forms the remaining 70% of original exergy into electricity, and we assumefor the thermodynamic, exergetic, efficiency of this conversion process 50%,which compares to a thermal efficiency of 55% for some of the best pow-erstations in the world. Next we consider the loss for transportation of theproduced electricity to the consumer and estimate this loss at about 6%. Sowe arrive at a number close to one third of the original exergy that is nowavailable for the customer to run his or her refrigerator, washing machine,and so on. That is why Yoda [2] in his book Trilemma writes a chapter withthe title: ‘‘66% of our energy is being wasted.’’ It is indeed shocking that dueto our technical limitations we are not able yet to explore the exergyavailable for more than 35%. At this point we must draw attention to thefact that instead of 35% we often read numbers close to 50%. This is aconsequence of the fact that such sources take as reference point the heatavailable in the combustion gases and start their calculations from there,ignoring the exergy loss incurred in the combustion step from the originalchemical exergy of methane to the products of its combustion.

Let us have another look at Fig. 5. It allows us to make a number ofinteresting observations. First of all, it is an illustration of the first law. Byintroducing one mole of methane, we introduce an amount of energy,chemical energy, to the amount of some 830 kJ. This amount is fully avail-able for work, but in the process that follows we are not able to recover allthis energy for work. Instead this available work is partly converted intowork dissipated, lost work, apparent as heat transferred to the environmentat T0 and P0. However, the sum of available work and lost work remainsconstant, the law of conservation of energy. This is what Baehr [16]formulated as, ‘‘The sum of Anergy and Exergy is constant.’’ Second, thecurve depicting the decrease in available work during the process is anexpression of the second law, showing that the quality of energy (see Chap-ter 6) is decreasing over the process in the direction of the process. Baehr’sdefinition of the second law was, therefore, ‘‘Exergy can always be con-verted into Anergy. Anergy can never be converted into Exergy.’’

A third observation is that the use of a fossil fuel contributes to thedepletion of our resources, as their supply is finite. Because this energysource is a material source of energy, embodied in compounds mainlymade up of carbon and hydrogen, we are bound to material emissions, of

Chapter 13184

which CO2 is the most prominent product. After our excursion in Section 2to biology, it strikes us that the material flows of emission and extractiondo not participate in closed cycles, at least not to the extent that re-generation can keep up with consumption. Last but not least, the obser-vation can be made that for the purpose of the powerstation, which is toproduce electrical energy, strictly speaking, no material source of energy isrequired. Our conventional way to produce electricity is to use a materialfuel, but, as a simple photovoltaic cell illustrates, radiation, as an imma-terial source of energy, can produce electricity as well, and this withoutmaterial emissions.

Figure 6 tries to express that the work originally available in fossil fuelis used to ‘‘turn the wheel’’ for most of our global energy needs and is lost intime, while the mass in which this work was embodied is conserved andemitted. In the process the mass and energy are conserved, but the quality ofthis energy diminishes, expressed in the fainting ‘‘color’’ of the energy flow.

In contrast, Fig. 7 expresses that for the same global exergy dissipa-tion, the sun as the energy source can be exploited without the need formaterial emissions. Of course, this assumes that the solar exergy reachingour earth exceeds that of the earth’s exergy needs. Although this appears to

Figure 6 The fate of fossil fuels.

Figure 7 A solar-fueled globe.

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be the case [3], some serious reservations have been made [17] by those whohave looked into man’s so-called ecological footprint. We return to thissubject in Section 5.

It is interesting to realize that, eventually, all exergy in the sun’s ra-diation to the earth is dissipated. Heat released to the environment, withoutexergy, will be radiated into the environment, being a source of exergy forany body lower in temperature. In this way the earth’s steady-state tem-perature is maintained [18]. If the original solar exergy were partly tappedfor exploiting it for our industrial activities, the same amount of entropywould eventually be produced, but for this part with some delay in time.

5 ECOLOGICAL RESTRICTIONS

‘‘This world provides enough for everybody’s need but not enough for

everybody’s greed.’’—Mahatma Gandhi (1869–1948)

The previous sections have pointed to the important role that solarenergy will play in a sustainable society.Whether we talk of a living system, anindustrial society, or an economic system, it seems that ultimately solar energyshould drive it: ‘‘The sun is our nuclear reactor, remote and safe’’ [3]. In thatcontext it makes much sense to pay attention to an inspiring and conscious-ness-raising monograph with the imaginative title Our Ecological Footprint[17]. The ecological footprint ‘‘accounts for the flows of energy and matter toand from any defined economy and converts these into the correspondingland and water area required from nature to support these flows.’’ It is ‘‘ameasure of the load imposed by a given population on nature. It representsthe land area necessary to sustain current levels of resource consumptionand waste discharge by that population.’’ An analysis based on this conceptleads to an estimate of the ‘‘ecologically productive area’’ required for theresource consumption and waste assimilation of a defined population inorder to sustain its existence. The monograph’s authors expect that thisconcept can be applied as ‘‘a planning tool that can help to translatesustainability concerns into public action.’’

The authors start by making an estimate of the ecologically productivearea that globally is available. The earth has a surface area of 51 billionhectares (ha), of which 14.5 billion ha are land. Only 8.9 billion ha of landare believed to be ecologically productive, that is, can perform functionsvital to human activities. A fair earth share is the amount of land eachperson would get if all ecologically productive land on earth were dividedevenly among the present world population. As of writing this book, theworld population is about 6 billion people. This corresponds to an earth

Chapter 13186

share of about 1.5 ha/cap. If the uncertain growth of the earth’s ecologicallyproductive area cannot keep up with the certain and expected growth of theworld population in the next 40 years or so, this share may even decrease toas low as 1 ha/cap.

Next the authors try to come to a fair estimate of what they have definedas the ecological footprint. They start from the assumption ‘‘that everycategory of energy and material consumption and waste discharge requiresthe productive or absorptive capacity of a finite area of land orwater.’’As truesports and Canadians they have selected Canada as their first nationalexample. They have constructed a so-called consumption–land-use matrixwith consumption categories as food, housing, transportation, and so on andcorresponding land-use categories for energy, crop, pasture, and so forth. Inthis way they arrive at an ecological footprint for Canada of 4.3 ha/cap! In thesame way it can be calculated that the ecological footprint of the UnitedStates is 5.1, of Australia 3.7, of Japan 2.0, and of India, as yet, 0.4 ha/cap.For the world as a whole the calculation is 1.8 ha/cap! Then the authorsestablish the ecologically productive area per capita that each country hasavailable and recognize the need to define the so-called ecological deficit.Canada and Australia take the exceptional position of having a surplus withproductive areas of 15.2 and 32.2 ha/cap, respectively, but theworld as awholeturns out to have a deficit, 1.5 ha/cap as opposed to 1.8 ha/cap. The UnitedStates has a deficit of 80% (2.8 ha/cap available as opposed to the 5.1 ha/capconsumed), and a country like The Netherlands even has a deficit of 1900%.Most of this country’s ecological footprint, like that of so many otherdeveloped countries, is thus made beyond the region where its population isliving. If we take the concept of the ecological footprint seriously, then oneimportant conclusion of the authors’ analysis should concern us: 20% of theworld’s population consumes up to 80% of the world’s resources, andtherefore the developed world alonemakes an ecological footprint larger thanthe ecologically productive area that the globe currently has available. This iswhat the authors call the global ecological overshoot: It seems that ‘‘there isnothing left into which the rest of the world can grow.’’There is a striking anddeceptive correspondence with Susan George’s glass of champagne symbol-ism, Fig. 8 [19]. If the contents of the glass represent theworld’s gross domesticproduct, then the bottom 1% is produced by 20% of its citizens, the poorest,whereas the top 80% is produced by another 20% of its citizens, the richest.

Of course, a concept with such dramatic implications for the state ofthe world has been the subject of great scrutiny, and an illustration is thediscussion that has been published in the Journal of Ecological Economics[20]. Experts have expressed both serious criticism and support on the as-sumptions made and the analysis applied. But we believe that the conceptremains one of great illustrative power and cannot be ignored in anydiscussion on sustainable development. As recently as early 2002, the

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famous sociobiologist Edward O. Wilson [22,23] discusses this concept in hisbook The Future of Life [22], which has been reviewed in Scientific American[23]. He mentions an ecological footprint of 1 ha/cap in developing nations,but 9.6 ha/cap in the United States, while the average footprint worldwide is2.1 ha/cap. He concludes that with existing technology we would requirefour more planet earths to reach present U.S. levels of consumption. Theleast one can say is that it can contribute to create wide public awarenessand act like a warning light. Wackernagel and Rees [17] conclude by statingthat, ‘‘What we lack is intellectual and emotional acceptance of the fact thathumanity is materially dependent on nature and that nature’s productivecapacity is limited.’’ Therefore, dematerialization of economic goods andservices must proceed faster than economic growth. They have estimatedthat a drastic (4–10-fold) reduction in material and energy intensity per unitof economic output is required for global sustainability.

In the above studies it has become apparent that energy consumption isan important part of the ecological footprint. For example, for Canada nearly60% of the footprint stems from the need for energy. Therefore, the authors[17] also studied the productivity of various energy sources in a sustainableeconomy. From these studies it appeared that solar energy as in photothermaland photovoltaic conversions or as in wind energy is close to 10 times moreefficient than fossil fuel. This source of energy would therefore fit well withinscenarios for sustainable development but also calls for new technology.

6 THERMODYNAMIC CRITERIA FOR SUSTAINABILITYANALYSIS

Sustainability is a critical issue and the word is often bandied about. How-ever, how can we measure whether a process is genuinely sustainable? This

Figure 8 Susan George’s glass.

Chapter 13188

section relates to the evolution of a model that can be used to help decide onthe sustainability of a given practice and is based on two of our earlierpapers [14,24]. Key advances include the quantification of renewabilitybeyond a renewable/not renewable basis.

6.1 Introduction

Industry is under increasing pressure from governments and environmentalgroups to improve the sustainability of its processes. However, how thishigher level of sustainability should be achieved is not really clear, and eventhe definition of sustainability is often only qualitative, as we have seenearlier. There is a need for a tangible quantitative description that allows thesustainability of technological processes to be systematically evaluated,compared, and improved.

In earlier work by De Wulf et al. [24] we showed that different aspectsof process sustainability can be quantified by using thermodynamic princi-ples. Indeed, the thermodynamic concept of exergy is used as the basis for theconstruction of sustainability parameters, which conveniently express par-ticular aspects of process sustainability on a scale of zero to one. Elements ofthis work were used to analyze the sustainability of several industrial pro-cesses, and new insights have led to some meaningful improvements.

All real processes must consume exergy to proceed, and this meansthat all our technological activities are ultimately limited by our ability tosupply exergy to our processes. The only exergy that can be considered astruly sustainable is the exergy supplied by solar radiation, because this so-lar exergy will be available on a very large time scale and its immaterialnature allows processes using it to operate within closed material cycles onearth.

However, our potential to use solar exergy is limited. Although thetotal amount of exergy reaching the earth as solar radiation is enormous,this exergy is dispersed over a very large area and its effective harvesting islimited to relatively few sites. These sites are often also the areas needed foragriculture, living space, and industrial activity and too intensive harvestingof solar exergy can be disruptive to the natural environment. For instance,large-scale introduction of solar panels can alter the natural heat absorptionof the surface and it thereby has the potential to alter local climates.

It is clear that ultimately our only limitation to sustainable productionis obtaining the exergy to run the production processes and to drive closedmaterial cycles. In view of this, exergy can be considered the ultimate scarceresource in our technological processes, and exergy flows to or from theseprocesses are therefore vital elements of a method aiming to quantifyprocess sustainability. Our first attempts to use exergy flows in the con-struction of sustainability parameters were published by De Wulf et al. [24].

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This original quantification method is the basis for our newly developedmethod, which expresses the sustainability of technological processes in a setof three independent sustainability parameters. These three parameters dealwith the resource utilization, the energy conversion, and the environmentalcompatibility of the process, respectively. The second and third parametersare revised elements of the work of De Wulf et al. [24], while the definition ofthe first parameter is entirely different. The parameters are discussed sep-arately in the following sections.

6.2 Sustainable Resource Utilization Parameter AA

One of the major factors undermining the sustainability of a productionprocess is the depletion of the resources it uses. A quantification of processsustainability should therefore include a parameter that deals with thesustainability of resource utilization, and the construction of such a param-eter begins with defining a quantitative measure for the depletion of anindividual resource. One way of doing this is to classify each resource as eitherrenewable or nonrenewable, as was done by De Wulf et al. [24]. Thedistinction made between renewable and nonrenewable resources is thatrenewable resources are created at least as fast as they are consumed (e.g.,solar energy), while nonrenewable resources are consumed faster than theyare created (e.g., crude oil).

However, there are two major problems with this renewability con-cept. First, the idea of a resource being either renewable or nonrenewableseems somewhat artificial. Even the sun is depleting a finite amount ofnuclear fuel, and it is therefore dubious to regard solar energy and derivedenergy sources such as wind- and hydro-energy as completely renewable.Also, so-called nonrenewable resources such as fossil fuels or mineraldeposits are being formed naturally to some extent, and therefore they arenot entirely nonrenewable. Obviously, the renewability of resources is moregradual than suggested in the black-and-white representation of renewableversus nonrenewable, and a parameter expressing the sustainability ofresource utilization should account for these more subtle differences inresource renewability.

A second objection that can be made against the renewability conceptis that renewability is only a part of sustainable resource utilization, since itdoes not involve the natural reserves of resources. Although the concept ofrenewability rightfully views the consumption rate of a resource in relationto its production or regeneration rate, this gap between consumption andregeneration rate should in turn be viewed in relation to the size of thenatural reserves of that resource. In fact, a temporary discrepancy betweenthe consumption and the regeneration rate of a resource does not necessarily

Chapter 13190

threaten the sustainability of a process when the resource is plentiful. Ofcourse, not having certain material cycles closed can have a profound effecton the natural environment (e.g., via harmful emissions), but this is beyondthe scope of this particular sustainability parameter, which deals only withresource depletion.

Hence, instead of considering the renewable versus the nonrenewableresources in a process, it is preferred to quantitatively combine the con-sumption rate (fm,consumption), the regeneration rate (fm,production), and theextent of natural reserves (Mreserves) of a resource, as they are known at thistime, in a resource depletion time (H ) defined as

s ¼ Mreserves

fm;consumption � fm;productionð1Þ

Besides taking into account any gap between the consumption and regen-eration rate of a resource, the depletion time relates this gap to the extent ofthe natural reserves. The depletion time is then a measure for the rate atwhich the currently known reserves of a resource are being depleted. Forexample, a depletion time of 100 years means that currently 1% of theknown reserves is being depleted yearly; likewise, a depletion time of 1000years means that yearly 0.1% is being depleted. It should be stressed that thedepletion time as defined in Eq. (1) does not attempt to predict resourcedepletion in the future; it merely indicates how fast a known supply of aresource is currently being depleted.

This definition means that the depletion time of a resource is time-dependent. The consumption rate of a resource may increase over time as aresult of increased industrial production, or it may decrease if alternativeresources are increasingly being used. Likewise, the regeneration rate mayincrease when more resources are recycled, and reserves may shrink afterprolonged utilization or may expand when new natural deposits are found.In addition, more accurate data may become available, for example on theextent of currently known reserves or on the natural formation rates ofcertain deposits. In any case, the depletion time H is variable, and it reflectsthe rate of resource depletion only in the present situation.

The depletion time of a resource obtained with Eq. (1) cannot be useddirectly in the construction of the sustainability parameter and, therefore, itis first converted to a factor that can be viewed as an expression of resourceabundance on a scale of zero to one (Fig. 9). For a resource i with a de-pletion time H i, the abundance factor ai is defined as

aiusi

si þ s0

� �ð2Þ

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The reference time H 0 in Eq. (2) represents the resource depletion time atwhich the abundance factor ai is at the value of exactly one half (i.e., 50%).This reference time H 0 must be given an appropriate value at which thefactors ai adequately reflect the differences in the abundance of real re-sources. For example, a reference time H 0 of 1000 years will give fossil fuelsabundance factors roughly ranging from 0.1 to 0.5, while sunlight, probablyavailable for billions of years, will have an abundance factor approachingunity.

Important to note is the asymptotic behavior of Eq. (2), which isclearly seen in Fig. 9. This nonlinearity causes the abundance factor ai to bemore sensitive at small depletion times and less sensitive at large depletiontimes, which is in accordance with our intuitive judgment. When comparingtwo different natural resources, the difference between 100 and 1000 years ofdepletion time is much more important than the difference between 1 billionand 10 billion years. The latter time scales are both so large that it is almostequally unlikely that the depletion of either one of these resources will causea process using them to become unsustainable. Hence, the nonlinear be-havior of Eq. (2) brings some common sense to the quantification method.

With the abundance factors as quantitative measures for the abun-dance of individual resources, the focus can now be on expressing the sus-tainability of multiple-resource utilization in a particular technologicalprocess. The first step is to determine how available are, on average, all

Figure 9 Graphical representation of Eq. (2). Abundance factor as a function ofdepletion time.

Chapter 13192

the resources used in the process. This average abundance (aaverage) isobtained by averaging the abundance factors (ai) of the individual resourceswhile using their exergy flows (Exin,i) to the process as averaging weights(Fig. 10):

aaverage ¼

Xi

ai � Exin;iXi

Exin;i

ð3Þ

Equation (3) uses the exergy flows of the resources because these valuesexpress the minimum amount of work required to produce these resourcesfrom compounds that are thermodynamically in equilibrium with the naturalenvironment. As ultimately only exergy is scarce, the exergy flows ofresources are better indicators of relative importance than their mass orvolume flows.

Although very useful, the average abundance of resources (aaverage)alone is not capable of adequately expressing the sustainability of resourceutilization. As a result of the averaging procedure, small abundance factors,which come from resources that are rapidly being depleted, can be (partly)compensated by large abundance factors, which come from resources that aredepleted relatively slowly. In this way, the weakest link in the chain, namelythe resource being depleted at the highest rate, does not act as a barrier to thesustainability of the resource utilization in a process. This opposes commonsense because a process already becomes unsustainable when only one of theresources it requires is depleted.

This problem can be solved by looking not only at the average re-source abundance, but also at the minimum resource abundance. Minimum

Figure 10 The sustainability parameter a is based on the average abundance factoraaverage, which considers all the abundance factors ai and exergy flows Exi of theindividual resources used in the process.

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resource abundance (amin) can be defined simply as the smallest of theresource abundance factors ai relevant in the process:

amin ¼ min|{z}i

ai½ � ð4Þ

With amin we have identified the weakest link in the chain of resources usedin the process, and this can be used to limit the effect of the averageabundance factor (aaverage). Hence, the parameter for sustainable resourceutilization (a) can then be defined as the product of the average (aaverage) andthe minimum (amin) abundance of resources:

a ¼ aaverage � amin ð5ÞIn this way, the sustainability parameter a includes the depletion rates of allresources used in the process (via aaverage), while, at the same time, it isdirectly limited by the resource with the highest depletion rate.

The proposed method for quantitatively describing the sustainabilityof resource utilization in a process has several advantages. First, it considersthe degree of resource renewability, which allows even subtle differences inthe depletion of different resources to be accounted for. Second, it alsoincludes the (natural) reserves of resources, making the method yet morerefined. Finally, the concept of depletion times and their translation toabundance factors allow the resource sustainability parameter a of a processto be limited by its most rapidly depleting resource, which is quite realistic.

Example. Consider the following hypothetical process. Suppose aprocess can be driven by three different sources of exergy: oil, coal, and solarenergy. Using their current consumption rate, regeneration rate, and extentof natural deposits, the depletion times of oil and coal are calculated [Eq.(1)] to be 150 and 1000 years, respectively. For solar energy the depletiontime equals the lifetime of the sun, which is approximately 5 billion years(Table 2).

Taking the reference depletion time H 0 at 1000 years, the depletiontimes of oil and coal yield abundance factors of 0.13 and 0.50, respectively;the very large depletion time of the nuclear fuel in the sun leads to anabundance factor for solar energy that approaches unity (note that theabundance factor is less sensitive at high depletion times and that this isconvenient because higher depletion times can usually be determined lessaccurately).

With Eqs. (3)–(5), and with the abundance factors for oil, coal, andsolar energy as determined above, it is possible to determine the parameterfor sustainable resource utilization for a process that uses solely one or moreof these three resources. Table 3 lists the relevant data for several such

Chapter 13194

processes, each extracting different percentages of the total required exergyfrom oil, coal, and solar energy.

First of all, Table 3 lists three processes that each extract their exergyentirely from one of the three resources (processes 1, 2, and 3). In thesesituations, there is only one relevant abundance factor, and its value thensolely determines the values of the average and minimum abundance factor.Also, the sustainability parameter is then simply this value squared. Theresults show that the process using only oil (process 1) is the least sus-tainable in its utilization of resources, the process using only coal (process2) is more sustainable, and the process extracting all exergy from solarenergy (process 3) is practically entirely sustainable in terms of resourceutilization.

Table 3 also lists three processes (processes 4, 5, and 6) that extract adecreasing percentage of the total required exergy from the least durableresource oil, and an increasing percentage from the more durable resourcescoal and solar energy. Correspondingly, the average abundance factorincreases, also causing the value of the sustainability parameter to rise. How-ever, the minimum abundance factor remains the same since all threeprocesses use oil to some extent, which has a relatively small depletion time

Table 3 Relevant Data on Sustainability of Resource Utilization in Processes

Using Oil, Coal, and Solar Energy

Process Oil [%] Coal [%] Solar [%] aaverage amin a

1 100 0 0 0.13 0.13 0.022 0 100 0 0.50 0.50 0.25

3 0 0 100 f1 f1 f14 50 50 0 0.32 0.13 0.045 20 50 30 0.58 0.13 0.076 10 0 90 0.91 0.13 0.12

7 0 10 90 0.95 0.50 0.48

Table 2 Depletion Times and Abundance Factors of Oil, Coal,and Solar Energy

Exergy sourceDepletion time

[years]Abundance factor

[-]

Oil 150 0.13Coal 1000 0.50

Solar energy 5 billion f1

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of only 150 years. The values of the parameter rightfully indicate that usingmore durable resources helps to increase the sustainability parameter, butthat its effect is limited, because the weakest link, namely the least durableresource, is not completely replaced. In fact, process 7 in Table 3 illustratesthat when the use of oil in process 6 is replaced by coal, the sustainabilityparameter indicates a much more sustainable use of resources.

The effect of the minimum abundance factor amin on the sustainabilityparameter a may seem counterintuitive. However, it must be realized thatthe sustainability parameter a only expresses that part of process sustain-ability that involves the availability of the resources used. The fact thatprocess 6 in Table 3 may be more sustainable than, for example, process 2 interms of environmental impact is not relevant to this particular aspect ofprocess sustainability. Purely in terms of resource utilization, process 2 ismore sustainable than process 6, because process 2 does not depend on arapidly depleting resource like oil.

6.3 Notes on Determining Depletion Times andAbundance Factors

A special situation in the determination of depletion times and abundancefactors occurs when a resource used in a process is actually a half-product;for example, iron metal is not a naturally occurring resource but is producedfrom iron ore in a blast furnace. The abundance factor of such a half-product must then be derived from the smallest depletion time among theresources used during its production. Since the abundance of, for example,iron metal is limited by the abundance of heavy oil fractions, which are usedto convert coal into cokes, the abundance factor of iron metal can be basedon the depletion time of oil.

Another special situation arises when one resource has its origin in twodifferent processes. For instance, when a process uses the electricity pro-vided by an energy company, it is possible that this electricity is generatedpartly by burning coal and partly by burning natural gas. In this case, theprocess should be considered to use two different types of electricity:electricity from coal and electricity from natural gas. Both types of elec-tricity then have their own derived depletion time and, based on how muchthey contribute to the total amount of electricity supplied, their own exergyflow.

Finally, the concept of depletion times, as it is used in the constructionof the sustainability parameter, is also suitable to include the sustainabilityof production of facilities needed to harvest resources. For instance, solarenergy may in principle have a depletion time of billions of years, butthe production of photovoltaic cells usually requires some very scarce

Chapter 13196

elements for which the depletion times are much smaller. The sustainabilityof using solar energy harvested with photovoltaic cells should then be basedon these latter depletion times and not on the depletion time of solar energyitself.

6.4 Exergy Efficiency H

The efficiency parameter focuses on the conversion of energy in the processitself (Fig. 11). Since exergy rather than any other resource is the ultimatelimiting factor to production activities, a process is most sustainable when ituses the exergy of its ingoing resources most efficiently. For this reason, theexergy efficiency of the process is important enough to be considered as aseparate sustainability parameter:

D ¼P

Exout;usefulPExin;process

ð6Þ

Equation (6) explicitly mentions the useful exergy flows coming out of theprocess because exergy can be lost in two different ways. First, exergy is lostin any real process as a result of irreversibility in the process itself, and suchlosses are called internal exergy losses. Second, exergy can be lost via wastestreams that are not yet at equilibrium with the natural environment.Examples of such external exergy losses are the release of hot flue gasesor high-pressure gas to the atmosphere. Both the internal and the externalexergy losses are in principle inefficiencies, and the exergy used efficiently inthe process is therefore only the exergy of products and the exergy of wasteproducts provided they are made useful in other processes.

Figure 11 The sustainability parameter D is the efficiency with which the exergy of

resources is transferred to the products of the process.

Sustainable Development 197

6.5 The Environmental Compatibility x

A third main aspect of process sustainability is not damaging the naturalenvironment, and the environmental parameter n as defined by De Wulf etal. [24] elegantly quantifies this part of process sustainability. Its basic idea isthat negative effects of a process on the environment must be abated beforethey can do damage to the natural environment. The extra exergy requiredto achieve this abatement then reflects the environmental incompatibility ofa process to the natural environment (see Fig. 12).

It should be noted that abating negative effects is a very broadconcept. Abatement not only applies to emissions, as considered by DeWulf et al. [24], but can also apply to all kinds of negative effects, includingthermal pollution or even extraction of resources from the environment.Examples of harmful effects of resource extractions are erosion of soil aftercutting down forests or subsidence of ground after extraction of natural gasor oil from underground deposits. Abatement is required for all effectsconsidered harmful to the environment that occur either during the processor during the eventual destruction of the products after their use.

Based on the exergy required for abatement, the sustainability param-eter expressing the ecological compatibility of a process is defined as given inEq. (7):

n ¼ Extotalin;process

Extotalin;process þ Ex

totalin;abatement

ð7Þ

Figure 12 The sustainability parameter n expresses the exergy required to abate allthe effects of the process that are harmful to the natural environment.

Chapter 13198

The parameter n relates the exergy required to run the process to the exergyrequired to run the process in an environmentally sound way, whichincludes the extra exergy required for abating the harmful effects on theenvironment. A large exergy demand for abatement leads to a small valuefor the environmental parameter n, indicating that the process has a smallcompatibility with the natural environment. Only if a process requires noexergy for abatement, the environmental parameter n=1 and the process isconsidered completely compatible with the natural environment.

6.6 Determining Overall Sustainability

De Wulf et al. [24] combine individual sustainability parameters to form oneoverall sustainability coefficient S. However, although a single expressionfor the sustainability of a technological process may seem appealing, it hassome serious disadvantages.

First, one sustainability coefficient falsely suggests that sustainability isone-dimensional, and this undermines the idea that there are differentaspects to a complex concept such as sustainability. Second, a lot of valuableinformation is lost when merging the individual parameters into one overallcoefficient; the combination basically means that concrete and meaningfulexpressions are merged into an overall expression without a tangiblemeaning. The overall coefficient merely expresses something vague as theoverall sustainability of a process. Third, the method used to combine thethree individual parameters is highly subjective. Many methods of combin-ing parameters may be applied, such as several different averaging techni-ques or a least-squared method, but every method unavoidably involves avalue judgment on the relative importance of the different aspects ofsustainability.

Hence, to keep the quantitative expression of process sustainability asmeaningful as possible, separate sustainability parameters should not becombined into one overall sustainability coefficient. Expressing the sustain-ability of a process quantitatively is always a tradeoff between completenessand surveyability; one aims to lose as little valuable information as possible,but at the same time the expression of process sustainability must be conciseand well organized. It is felt that the three sustainability parameters asdefined in this chapter do exactly that and that the sustainability of a processis therefore best evaluated by independently considering these quantifica-tions of three fundamentally different aspects of process sustainability.

6.7 Related Work

We wish to conclude this section by referring to some related work. Ourformer student Wassenaar [25] has defined the fossil load as the percentage

Sustainable Development 199

of fossil exergy input of the exergy of the final product. He calculated 9%for fresh potatoes from ‘‘ecological’’ agriculture and 13% from convention-al agriculture, 64% for fresh French fries, and 80% for frozen French fries.

Gerngross and Slater [26] asked the question how green are greenplastics and show that in some cases less fossil energy is required per unitproduct if this is produced conventionally from nonrenewable resourcesthan when it is produced from a renewable resource, such as corn.

Berthiaume et al. [27] introduce the so-called renewability indicatorrelating the work produced from solar energy to the work required to re-store the degraded products from nonrenewable origin. Based on theiranalysis and making use of concepts such as the thermodynamic cycle, ex-ergy, and exergy consumption, they conclude that the process to produceethanol from corn is not sustainable as it requires more work of restorationthan is produced.

Finally, Brown and Ulgiati [28] have developed indicators to monitoreconomies and technology on their performance in sustainability. They makeextensive use of the concepts emergy and transformity, which have beenintroduced by two pioneers in ecological engineering, namely E. G. and H. T.Odum [29]. Both concepts show a remarkable resemblance with exergy andcumulative exergy consumption but are more specifically related to solarenergy and its absorption in ecosystems.

7 CONCLUSIONS

As the growth of the world population and of the average living standardsare certainties, so are economic growth, the growing need for resources, andthe increasing burdening of the environment. The environment is neither aninfinite supplier of resources, nor an infinite absorber of waste. Prominentpeople and reports therefore call for a global sustainable development wheresociety develops in harmony with the earth, with nature. But it seems thathowever good the intentions of the advocates of such a development are,they are not always aware of the implications and consequences thereof.This becomes clearer if we analyze nature itself in its cyclic behavior.

Nature seems to provide us with a true example of sustainability: tomake use of renewable resources, solar energy or heat from the inner earth,closing material cycles by making waste a feedstock for another actor in thecycle and doing all this with a remarkable efficiency. The ‘‘cycle of life’’ is athermodynamic cycle producing mechanical, chemical, and electrical energy,driven by an immaterial source of exergy while making use of a ‘‘workingfluid’’ that changes in composition depending on its position in the cycle.The cycle produces solely immaterial emissions, that is, radiating waste heat

Chapter 13200

into the universe. This process is strictly irreversible, dissipative, andunidirectional, transforming what is useful—work—into what is useless—heat of the environment—and delayed by the creation, maintenance,activity, and degradation of living systems.

Economic and industrial systems share many features with livingsystems but differ markedly from them in the sense that useful work isextracted from nonrenewable, material resources and useless heat is emittedtogether with material waste products. As the earth is a closed system formatter, this shall ultimately lead to the exhaustion of resources and the accu-mulation of waste products. These systems should therefore rely increasinglyon renewable resources while simultaneously closing material cycles. Eventhen the constraint of the limited availability of ecologically productive areamay exist, as the originators of The Ecological Footprint have propagated.

A last conclusion is that thermodynamics as the ultimate accountantof the conversion and storage of energy and matter can provide thefundamental tools to assess to what extent an industry and even an economyare sustainable.

REFERENCES

1. Brundtland, G.H. Our Common Future, The World Commission on Environ-mental Development; Oxford University Press: Oxford, 1987.

2. Trilemma: Three Major Problems Threatening World Survival. Yoda, S., Ed.;Central Research Institute of Electric Power Industry: Tokyo, 1995.

3. Okkerse,C.; vanBekkum,H.Towardsaplantbased-economy?InStarch96—TheBook, Carbohydrate Research Foundation; The Hague: The Netherlands, 1997.

4. Harmsen,G.J. Inaugural address, Delft University of Technology, January 1998.

5. Moody Stuart, M. Newsweek, 1999.6. Tabaksblatt, M. Sustainability as a challenge. Speech at the occasion of the

Unilever Research Awards, 1999.

7. Merkel, A. The role of science in sustainable development. Science 17 July1998, 281, 336–337.

8. Ayres, R.U.; Simonis, U. Industrial Metabolism, Restructuring for SustainableDevelopment; United Nations University Press: Tokyo, 1994.

9. InHarmonywith the Earth. Sawa, T., Ed.; Central Research Institute of ElectricPower Industry: Tokyo, 1996.

10. Nelson, D.L.; Cox, M.M. Lehninger Principles of Biochemistry; 3rd ed.;

Worth, MI, 2000.11. Lehninger, A.L. Bio-energetics. 2nd ed. W.I. Benjamin: Menlo Park, CA, 1973.12. Ayres, R.U. Eco-thermodynamics: Economics and the second law. Ecological

Economics 1998, 26, 189–209.13. Baumgartner, S. Ambivalent Joint Production and the Natural Environment;

Physica Verlag: New York, 2000.

Sustainable Development 201

14. Lems, S.; van der Kooi, H.J.; de Swaan Arons, J. The sustainability of resourceutilization. Green Chemistry 2002, 4, 308–313.

15. Energy Needs, Choices and Possibilities. Scenarios to 2050, Global Business

Environment, Shell International, 2001.16. Baehr, H.D. Thermodynamik. 6th ed; Springer-Verlag: New York, 1988.17. Wackernagel, M.; Rees, W. Our Ecological Footprint; New Society Publishers:

Gariola Island BC, Canada, 1996.18. De Vos, A. Endoreversible Thermodynamics of Solar Energy Conversion;

Oxford University Press: Oxford, 1992.

19. George, S. Citizenship and Solidarity in the Age of Globalization, TrilemmaSymposium; Central Research Institute of Electric Power Industry: Tokyo,1998.

20. Forum: The Ecological Footprint, Ecological Economics 2000, 32, 341–394.21. Gould, S.J. This view of life: Microcosmos. Natural History 1996, 105(3), 20–

23.22. Wilson, E.O. The Future of Life; Alfred A. Knopf: New York, 2002.

23. Wilson, E.O. The bottleneck. Scientific American, February 2002.24. De Wulf, J.; van Langenhove, H.; Mulder, J.; van den Berg, M.M.; van der

Kooi, H.J.; de Swaan Arons, J. Green Chemistry 2002, 2, 108–114.

25. Wassenaar, J.A. Sustainability of the potato production chain. A thermody-namical approach. Master’s Thesis. Delft University of Technology: Delft, TheNetherlands, November 2000; 38 pp.

26. Gerngross, T.U.; Slater, S.C. How green are green plastics. Scientific American,August 2000.

27. Berthiaume, R.; Bouchard, C.; Rosen, M.A. Exergetic evaluation of the re-

newability of a biofuel. Exergy Int. J. 2001, 1 (4), 256–268.28. Brown, M.T.; Ulgiati, S. Emergy based indices and ratios to evaluate sus-

tainability. Ecological Engineering 1997, 9, 51–69.29. Odum, H.T. Self-organization, transformity and information, Science 1988,

242, 1132–1139.

Chapter 13202

14Efficiency and Sustainability inthe Chemical Process Industry

1 INTRODUCTION

The process industry is a large consumer of raw materials, which are utilizedboth as feedstock for its numerous products and as an energy source to driveits various processes. In the scope of sustainable development, consensus onthe limited availability of our natural resources, and on the need for closedcycles in our ecosphere, has grown. Hence, the current approach of ourprocess industry is in question, in terms of both efficiency and sustainability.First we need to address the subject of efficiency. There is a need forquantitative figures on the efficiency with which natural resources areconsumed. Such quantitative figures can be provided from a thermodynamicanalysis of the process indicating the discrepancy between the ideal ther-modynamic process and the state of the art in current process technology.Next we will address the question of sustainability. Is it possible to indicatein quantitative terms to which extent a process or an industry is sustainable?

This chapter has been based largely on one of our earlier publications[1].

2 LOST WORK IN THE PROCESS INDUSTRY

In Part I we have defined the concept of lost work and identified it with theentropy production in the process. With the help of irreversible thermody-namics we have found its origin in the finite driving forces of the process. Wehave also introduced in Chapter 6 the concept of minimum work and shownhow this concept leads to a convenient thermodynamic tool called exergy, oravailable work. It was also shown that exergy analysis, also known as ther-

203

modynamic analysis, can give an insight into the amount and origin of lostwork and thereby into the thermodynamic efficiency of a process. Simpleillustrations were given in Chapters 6 and 8, while real case studies weredealt with in Chapters 9 to 11.

Exergy analysis has so far drawn most attention in the energy-systemarea, where heat is converted into power or electricity. It has penetrated lessinto the chemical process industry, perhaps because of its greater complex-ity. In real material conversion processes, primary materials, naturalresources, are converted into consumer materials and heat. These processesdo not proceed ideally, so part of the work available in the primary ma-terials will be lost. To obtain a ‘‘feeling’’ for lost work in the process in-dustry, the production processes of several ‘‘large-quantity’’ products havebeen analyzed. This chapter only focuses on input and output streams of theconversion process; production of the natural resources, transportation, andstorage are excluded from the system boundary, because most often thelargest part of lost work is incurred in the conversion step. Elaborate lostwork analyses are given, for example, by Hinderink et al. [2] and Wall [3].Figure 1 illustrates the general result of a lost work analysis of a materialconversion process in a Grassmann diagram. A lost work analysis reveals

Figure 1 Grassmann diagram of a typical conversion process.

Chapter 14204

Table

1ResultsofGlobalLost

Work

AnalysesofSeveralIm

portantProductionProcesses

Theoreticalwork

potential(kJ/molfinalproduct)

Final

product

Molecular

weight

Raw

materials

Data

taken

from

Technology

level

Raw

materials

Final

product

Steam

credit

Lost

work

Thermodynamic

efficiency

a(%

)

Hydrogen

2naturalgas/air

[4]

1990

409

236

28

145

58

Ammonia

17

naturalgas/air

[5]

1980

763

338

85

340

44

Aluminum

27

bauxite

[6,7]

1990

4703

888

n.a.

3815

19

Methanol

32

naturalgas/air

[8]

1985

1136

717

80

339

63

Oxygen

32

air

[9]

1980

64

4n.a.

60

6

Urea

60

naturalgas/air

[5,10]

1980

1590

686

150

754

43

via

ammonia

Nitricacid

63

naturalgas/air

[5,11]

1975

995

43

151

801

4

via

ammonia

Copper

63.5

copper

ore

[7,12]

1980

1537

130

n.a.

1407

9Methane

16

——

—830

——

——

aExcludingsteam

credit.

Efficiency and Sustainability 205

internal losses due to process imperfections, whereas an energy analysisdeals with losses in physical streams such as those of waste material and heatleaving the process.

The input side of such a process is represented by natural primary re-sources. No distinction has been made between resources used as feedstockand resources applied as fuel; they are all quantified by their exergy value,the universal measure. The output side is represented by the exergy of thedesired product(s) and of recovered useful heat, in the form of a steamcredit. By comparing the total amount of exergy entering and leaving theprocess, the loss in available work is revealed, which is due to either processinefficiencies or material/heat release to the environment, so internal andexternal losses are lumped. All data have been taken from publishedliterature (Table 1).

3 THE PROCESSES

Table 1 gives a ‘‘thermodynamic blueprint’’ of some large-scale productionprocesses. The numerical values presented refer to the technology level ofthe 1970s or 1980s and are based on primary, natural, resources only, suchas natural gas and air. Because only primary resources are allowed to enterthe processes, several subprocesses can be present inside the system, forinstance for the generation of intermediate products, or for the generation ofsteam or electricity. Lost work involved with the latter type of subprocessesis handled by using commonly applied thermodynamic efficiencies (e.g.,50% for power production via cogeneration).

An example of a process with an intermediate product is the ureaprocess. The second step, starting from ammonia, is over 90% efficient,whereas the total process, having ammonia just as an intermediate product,shows an efficiency of only half of this value. For the nitric acid process, Fig.2, the second step is the least efficient as indicated by the simplifiedGrassmann diagram in Fig. 3 for this process. However, an importantmessage that Fig. 3 conveys is that large losses occur in the conversionprocesses, namely the transformation of CH4 into NH3 and NH3 into nitricacid. Nitric acid has a low exergy content, and it is partly responsible for thelarge loss incurred in the conversion step. Losses, therefore, can also be auseful metric in the evaluation of processes and can be caused by processinefficiencies or a final product that is simply low in exergy!

Results of lost work analyses strongly depend on the system boundaryconsidered and the credit that is given to co-products and byproducts.Therefore, the analysis results can vary per author.

Chapter 14206

4 THERMODYNAMIC EFFICIENCY

Although efficiency values can be misleading because they can be defined innumerous ways [13,14], they are easy to handle. The definition of thermo-dynamic efficiency applied here is the ratio between the available work orexergy of the desired products, excluding useful heat, and the primary re-

Figure 2 Flowchart of a nitric acid process.

Figure 3 Simplified Grassmann diagram of the nitric process shown in Fig. 2.

Efficiency and Sustainability 207

sources applied. Usually, thermodynamic efficiencies based on lost workanalysis do not exceed 70% when starting from primary resources. At thehigher side of the efficiency range, the production of organic products can befound, while inorganic and metallurgical processes are at the lower side ofthe efficiency range. A combination of low efficiency and high input of ex-ergy indicates in general the need for process improvement. It is importantto distinguish between efficiency and lost work. Lost work refers to the pro-cess, and is related to the driving forces, whereas efficiency has to include the

Figure 4 Available and lost work for typical chemical processes.

Chapter 14208

exergy of the desired product. In the case of nitric acid, as we saw earlier, itis low. Lost work is an absolute metric, as opposed to efficiency, which is arelative metric. An overview of absolute lost work figures for the processindustry, such as shown in Fig. 4, is more distinct and can be of use to de-termine which products and/or which processes need to be reconsidered inview of sustainable development.

5 EFFICIENT USE OF HIGH-QUALITY RESOURCES

Figure 5 shows lost work figures for the utilization of natural gas for variouspurposes. From this picture it can be concluded that it is best to use naturalgas for those chemical processes in which its exergy eventually ends up in thedesired products. The basic rule behind this conclusion is that the degrada-tion of exergy has to be delayed as long as possible. This rule facilitates thechoice of chemical routes and raw materials. For the nitric acid process, thisrule is broken; the very high-quality raw material natural gas contributesnegligibly to the exergy content of the low-quality final product nitric acid.This suggests that an incredible drop in exergy takes place per atomN (NH3!HNO3) and perhaps an alternative chemical route should be sought, or thedrop in exergy should be utilized. Also, the direct use of high-quality natural

Figure 5 Lost work figures for the utilization of natural gas.

Efficiency and Sustainability 209

gas for low-quality heating purposes does not coincide with the idea ofsustainability.

6 TOWARD SUSTAINABILITY

In the discussion about how we should set up our chemical process industryin the near future, the sustainability issue is of prime importance. Sustain-ability in the ecological sense means that we do not place an intolerable loadon the ecosphere and that we maintain the natural basis for life. The com-plexity of the chemical industry with its numerous products has made us losesight of the associated ecological impact of these products’ life cycles: Whenyou produce something, you also produce long-term effects. In economicsthis concept is known as joint production [15], and we will discuss this inChapter 18.

Improvement of thermodynamic efficiency is frequently but errone-ously considered as the only contribution to sustainability. An increase ofthermodynamic efficiency, however, has to do with a lowering of the ratewith which our nonrenewable natural resources are consumed, whereas sus-tainability implies more than that, as we have discussed in Chapter 13.6.

Although the figures presented in this chapter are quite indicative, theydo not reflect the degree of sustainability of the process but rather its ef-ficiency. In other words, the extent to which the process uses renewablematerials is not given explicitly. Actually, a chemical conversion process canbe 100% efficient when all the originally available work ends up in the de-sired product(s). In real processes, exergy is lost. Hence, more exergy entersthe process than leaves it. This excess of exergy entering the process to makeit proceed has to originate from renewable sources, such as solar exergy, inorder to contribute to sustainability.

Such a ‘‘balanced’’ process industry can still lead to exhaustion of ournatural resources if the exergy content of the nonrenewable end productsis not utilized at the end of the product life. If we go one step further, ourstarting material should be renewable, for example carbon dioxide andwater. Real sustainable systems/chains need to be circular with respect tomatter; outputs should become inputs. The driving force for such a sus-tainable system must stem from solar energy, as we discussed in Chapter 13,which is essentially available in a large quantity. Wall [13] and Gong andWall [14] give elaborate discussions on exergy and sustainability.

Looking into this matter more carefully, we have come to the insightthat the extent to which a process contributes to sustainability can becharacterized by three parameters. One is the thermodynamic efficiency ofthe process. A second parameter needs to reflect the extent to which use hasbeen made of renewable resources. Finally, a third parameter is needed to

Chapter 14210

indicate the extent to which cycles have been closed. This has been discussedat great length in Chapter 13.6.

7 CHEMICAL ROUTES

The exergy of chemical components can be calculated from thermodynam-ics, as has been illustrated in Chapter 7. This exergy can be considered as theminimum work needed to synthesize the specific component from constit-uents of its surroundings. It has been shown that in practice the productionof desired chemicals requires far more work than indicated by the exergy ofthis desired product. In other words, the exergy entering and leaving suchprocesses do not balance, so work is lost. The challenge of our processindustry is to limit the losses, while still being able to let our processes runwith sufficient speed.

In past decades, increasing energy efficiency was accomplished mainlyby complex heat integration within existing chemical processes, requiringconsiderable investments. The thermodynamic or exergy analyses describedby Hinderink et al. [2], however, show that the chemical reaction step largelydetermines the overall thermodynamic efficiency. Chemical reactions havebeen found to be a notorious source of lost work. If chemical processes aredeveloped from scratch by state-of-the-art methods—namely, by structuredprocess synthesis procedures—attention can be paid to the core of the pro-cess, that is, the chemical reactions or the chemical reactor. Then, a sig-nificant improvement in energy efficiency and process economics can beachieved simultaneously [15].

Losses resulting from chemical reactions can be viewed in the sameway as losses resulting from heat exchange as we discussed in Chapter 4. Thedriving force for heat transfer is the temperature gradient, which determinesnot only the rate of transfer, but also the degree of devaluation of exergy.Chemical reactions also proceed along a gradient from high to low chemicalaffinity. On flowing along this gradient, heat is released and exergy is lost fora spontaneous chemical reaction. The relation between the Gibbs energy ofreaction and lost work is linear. This relationship has been established byDenbigh [16] and is discussed by Hinderink et al. [17]. This insight is ofprime importance for the development of future chemical routes [18].

For more sustainable chemical routes, chemical gradients should bereduced, or should be counterbalanced by chemical reactions proceedingagainst their gradient, a principle of which biological systems make exten-sive use [19]. In this view, there is an analogy between heat pinch andreaction pinch. Examples of reactions proceeding with a large gradient arethe production of nitric acid by the partial oxidation of ammonia and the

Efficiency and Sustainability 211

conversion of H2S into elemental sulfur and steam. The development of newchemical processes should thus focus on approaching exergy-neutral reac-tions. In addition, one should also look for sophisticated utilization of theGibbs energy of reaction [20], for example, by using it directly to drive aseparation, such as reactive distillation. Finally, although Fig. 4 is fairlyindicative, the graph lacks information on which part of the primary exergyis renewable. If, for example, the energy needed for the metallurgicalprocesses comes from hydro-energy, our conclusions with respect to theimprovement potential of these processes will have to be adapted.

8 CONCLUSIONS

Some general observations that can be made from lost work analyses are

The amount of lost work differs from product to product and fromprocess to process and depends largely on how skilled we are inprocess design.

Processes showing a large steam credit, albeit useful, should bedistrusted, because this implicitly means that more primary exergy isapplied than is actually needed.

All basic efforts to reduce lost work have to come from postponing aslong as possible the devaluation of exergy; preserve the quality ofenergy and matter.

With regard to process sustainability, the following observations can bemade:

The best source for exergy is a renewable resource.A more complete thermodynamic analysis of processes deals not onlywith the efficiency but also with the extent to which renewableresources have been used and to which extent material cycles havebeen closed.

A nonbasic approach toward efficiency and sustainability is in ourview unacceptable given the importance and urgency of these issues.Therefore, it is advisable to benefit from the quantitative power ofthe extended thermodynamic analysis proposed.

REFERENCES

1. Hinderink, P.; van der Kooi, H.J.; de Swaan Arons, J. On the efficiency and sus-tainability of the process industry, Green Chemistry, December 1999, G176–180.

Chapter 14212

2. Hinderink, A.P.; Kerkhof, F.P.J.M.; Lie, A.B.K.; de Swaan Arons, J.; van derKooi, H.J. Exergy analysis with a flowsheeting simulator. Part 2: Application:Synthesis gas production from natural gas. Chem. Eng. Sci. 1996, 51 (20),

4701–4715.3. Wall, G. Energy flows in industrial processes. Energy 1988, 13 (2), 197–208.4. Giacobbe, F.G.; Iaquaniello, G.; Loiacono, O. Increase hydrogen production.

Hydrocarbon Processing 1992, 3, 69–72.5. Cremer, H. Thermodynamic balance and analysis of syngas and ammonia

plant. ACS Symposium Series, 122; Washington, DC: ASME, 1980.

6. Habersatter, K. Okobilanz von Packstoffen stand. Schriftereihe Umwelt, 132;Bern: BUWAL, 1991.

7. Szargut, J.; Morris, D.R.; Steward, F.R. Exergy Analysis of Thermal, Chemical,

and Metallurgical Processes; New York: Hemisphere Publishing Corp., 1988.8. Supp, E. Improved methanol production and conversion technologies. Energy

Progress 1985, 5 (3), 127–130.9. Ullmann’s Encyklopaedie Der Technische Chemie, Band 20; Weinheim: Verlag

Chemie, 1981.10. Pagani, G. New process gives urea with less energy. Energy Progr. 1985, 5 (3),

127–130.

11. Lowenheim, F.A.; Moran, M.K. Industrial Chemicals; Wiley & Sons: NewYork, 1975.

12. Boustead, F.; Hancock, G.F. Handbook of Industrial Energy Analysis; John

Wiley & Sons: New York, 1979.13. Wall, G. Exergy—A useful concept within resource accounting. Report No. 77–

42; Goteborg, Sweden: Institute of Theroretical Physics. Chalmers University

of Technology, 1977.14. Gong, M.; Wall, G. On exergetics, economics and optimization of technical

processes to meet environmental conditions. Ruixian, C., Ed.; Proc. Intl. Conf.on Thermodynamic Analysis and Improvement of Energy Systems; China:

TAIES’97 Beijing, 1997; 453–560.15. Baumgartner, S. Ambivalent Joint Production and the Natural Environment;

Physica Verlag: New York, 2000.

16. Denbigh, K.G. The second law efficiency of chemical processes. Chem. Eng.Sci. 1956, 9 (1), 1–9.

17. Hinderink, A.P.; Kerkhof, F.P.J.M.; Lie, A.B.K.; de Swaan Arons, J.; van der

Kooi, H.J. Exergy analysis with a flowsheeting simulator. Part I: Theory; Cal-culating exergies of material streams. Chem. Eng. Sci. 1996, 51 (20), 4693–4700.

18. Ratkje, S.K.; de Swaan Arons, J. Denbigh revisited: Reducing lost work inchemical processes. Chemical Engineering Science 1995, 10, 1551–1560.

19. Lehninger, A.L. Bioenergetics, 2nd Ed.; W.I. Benjamin: Menlo Park, CA, 1973.20. Harmsen, G.; Hinderink, A.P. We want less: Process intensification by process

synthesis methods. Green, A., Ed.; 3rd Intl. Conf. on Process Intensification for

the Chemical Industry, Publication No. 38, Antwerp, Belgium, 23–28.

Efficiency and Sustainability 213

15Solar Energy Conversion

In this chapter we will focus on solar energy. After all, in terms of sus-tainability, fossil fuels compare less favorably with respect to supply andemissions, and as nature makes such abundant use of solar energy, itmakes sense to look at some characteristics of solar energy and its conversion.

Wholly in line with the approach in this book with regard to efficiencyand sustainability we will do this by performing a thermodynamic analysis ofwind energy (wind energy is ultimately driven by solar radiation), photo-thermal and photovoltaic energy conversion, and photosynthesis. We willstart by summarizing some characteristics of solar radiation. Most of thischapter has been based on the monograph Endoreversible Thermodynamics ofSolar Energy Conversion by Alexis de Vos [1].

1 CHARACTERISTICS

Solar radiation consists of photons of different energies E. Of particularinterest is the spectral distribution �nðEÞ, which describes how the photons aredistributed over the different energy values. The quantity �nðEÞ indicates thenumber of photons of specific energy E per unit surface area per unit energyper unit time. From this distribution we define the total photon flux as

�N ¼

Z l

0

�nðEÞdE ð1Þ

and the associated energy flux as

�E ¼Z l

0

�nðEÞEdE ð2Þ

215

Planck’s law expresses the spectral distribution �nðEÞ as a function of Eaccording to

�nðEÞ ¼ q � 2kc2h3

� E2

expE

kT

� �� 1

ð3Þ

in which q denotes the emissivity of the photon emission reservoir, c thevelocity of light, h Planck’s constant, and k the Boltzmann constant. Figure 1gives �n as a function of E with E in units kT and �n in units k2I2/c2h3, that is,m�2s�1J�1. This curve holds for an emissivity q = 1 when the spectrum iscalled a black-body spectrum. Note that the curve displays a maximum for anintermediate value of E, which is commonly referred to as Wien’s energy.Wien’s displacement law expresses that the coordinates of this maximumchange with temperature T. Figure 2 shows the Planck spectrum for threedifferent temperatures T = 5762 K, the temperature of the sun; T = 288 K,the average temperature of our planet; and T=2.7 K, the temperature of thecosmic background. The double-logarithmic scale allows for the clear visu-alization of how the three spectra are distributed over the most commonranges of light. From Planck’s law, Eq. (3), we can now proceed to Eqs. (1)and (2) and obtain the corresponding expressions for the photon flux

�N and

energy flux�E and find

�N ¼ qjVT3 ð4Þ

and�E ¼ qjT4 ð5Þ

Figure 1 The Planck spectrum with linear scales. E in units kT; �n in units k2T2/c2h3.

Chapter 15216

Both constants jV and j are expressions of and can be calculated from thenatural constants k, h, and c, which were discussed earlier. Equation (5),which relates the energy flux to the absolute temperature, is known as theStefan–Boltzmann equation. The coefficient j is known as the Stefan–Boltzmann constant. The average photon energy can be calculated from

��E ¼

�E�N¼ jT

jVð6Þ

and is found to be 2.70 kT.Finally, we should mention Kirchhoff’s law. The emissivity q expresses

which fraction a body of temperature T emits to bodies of lower temperature.If q=1, we speak of black-body radiation, otherwise of gray-body radiation.Kirchhoff’s law compares the emissivity q with the absorptivity a of a bodywhen exposed to incident radiation from a body with a higher temperatureand states that

aðEÞ ¼ qðEÞ ð7Þor when these properties are independent of energy

a ¼ q ð8ÞThe properties of solar radiation have been established from measurementsfrom a satellite, thus eliminating all influences from the earth’s atmosphere.From the measured Planck’s spectrum and by fitting Eq. (3), it can be con-cluded that the sun is a black body [2], that its emissivity q = 1, and that itstemperature is Ts = 5762 K. The sun emits a photon energy flux

�Es , and

Figure 2 The Planck spectrum with logarithmic scales (m.w: microwave; i.r: in-

frared; vis: visible light; u.v: ultraviolet radiation).

Solar Energy Conversion 217

therefore, the amount of energy emitted per unit time for 1 m2 of the sun’ssurface equals 1� �Es. The total energy emitted is obtained by multiplying thetotal external surface area with the flux: 4kR2

s emits a photon flux�Es; then the

total energy flow rate emitted by the sun is 4kR2s

�Es . However, when this

energy reaches earth, it is distributed over a much larger area, thus reducingthe energy flow rate. With R0 the radius of the earth’s orbit around the sun, 1m2 of the earth’s surface is irradiated by a flux

�Ee equal to

�Ee ¼ f

�Es ð9Þ

where the dilution factor f can be calculated from

f ¼ 4kR2s

4kR20

¼ R2s

R20

ð10Þ

and yields the numerical value of 2.6 � 10�5. From Eqs. (5) and (9) it followsthat

�Es ¼ fjT 4

s ð11Þwhich can be calculated to be 1353 W/m2. This radiation intensity from thesun upon the earth’s upper atmosphere is called the solar constant, S. Thecorresponding photon flux is

�Ne ¼ fjVT3

s ð12ÞThe average energy of one photon is

�E ¼ �

�Ee�Ne

ð13Þ

and is calculated to be 2.70 kTs = 1.34 eV.These results allow us to calculate the temperature of the respective

planets of our solar system by assuming that these planets prevail in thermalbalance, with the incoming energy of photons from the sun balancing theenergy of photons emitted by the planet. For the earth the incoming energyof radiation is

�Ein ¼ kR2

e ��Ee ¼ kR2

e � fjT 4s, with Re being the radius of the

earth and kR2e the surface area of the projection of our planet on a plane

perpendicular to the sun’s radiation. The energy emitted by our planetis�Eout ¼ 4kR2

e � jT 4e . By setting

�Ein ¼ �Eout , we can calculate the average

temperature of our planet from

kR2e � fjT 4

s ¼ 4kR2e � jT 4

e ð14ÞThe result is Te = 278 K, which corresponds reasonably well with thetemperature found from experiment, T exp

e = 288 K.

Chapter 15218

Repeating these calculations for the other planets of the solar systemgives a remarkably good correspondence between experimental and calcu-lated temperatures for the respective planets, save one notorious exception,namelyVenus! The experimental temperature is 733K, whereas the calculatedtemperature is only 327 K! This difference is caused by the pronouncedgreenhouse effect of its dense CO2 atmosphere. Introducing the number U asthe albedo of the planet and the number g as the greenhouse coefficient, Eq.(14) can be corrected for the fact that not all the sun’s incident energy isabsorbed, nor all the planet’s energy emitted:

1� Uð Þ � kR2p � fjT 4

s ¼ 1� gð Þ � 4kR2p � jT 4

p ð15Þ

with Tp being the average temperature of the planet concerned. With U=0.7and g=0.99 for Venus, the experimental temperature for this planet, T exp=733 K, agrees quite well with the calculated value of 765 K. Correcting bymeans of j and g for the earth results in a calculated temperature T calc

e = 289K, which is only 1 K above the experimental temperature of T exp

e = 288 K.This should have summed up themajor characteristics of solar radiation

that are relevant for the context of this book. For further details the interestedreader is referred to themonograph by Alexis de Vos [1] on which, as has beenmentioned in the beginning, most of the material presented above has beenbased.

2 THE CREATION OF WIND ENERGY

When one side of a planet is irradiated by the sun, the other side is not and atemperature difference is created. With the planet’s atmosphere as the work-ing fluid operating between the planet’s two extreme temperatures, macro-scopic cycles can be performed that act as the origin of winds. Gordon andZarmi [3] have generated the first model for this wind creation, which wassubsequently refined by De Vos and Flater [4]. Both models and their out-come will be briefly discussed in this section.

The sunny side of the planet is assumed to be a heat reservoir at tem-perature T3, the dark side is a reservoir at temperature T4. The illuminatedside is receiving energy from the sun, but is also emitting energy. The dark sideis emitting energy only. The net heat flow rate in sustaining the heat reservoirat T3 is

�Qin ¼ kR2

p � 1� Up

� �fjT 4

s � 2kR2p � 1� gp� �

jT 43 ð16Þ

Solar Energy Conversion 219

in which Rp, Up, and gp represent the planet’s radius, albedo, and greenhousecoefficient, respectively.

Of particular interest is�Qabsorbed , the total amount of solar energy

absorbed by the planet per unit time:

�Qabsorbed ¼ kR2

p � 1� Up

� � � fjT 4s ð17Þ

which is the first term in Eq. (16).At the cold side, with temperature T4, the planet emits energy with a

rate

�Qout ¼ 2kR2

p � 1� gp� � � jT 4

4 ð18ÞThe Carnot engine operating between these temperatures T3 and T4 with heatabsorbed at a rate

�Qin and rejected at a rate

�Qout will have an efficiency

D u�Qin � �Qout�

Qin

¼ 1� T4

T3ð19Þ

Equations (16) and (18) can be rewritten in the form

�Qin ¼ g1 T 4

1 � T 43

� � ð20Þand

�Qout ¼ g2 T 4

4 � T 42

� � ð21Þwith

T1 ¼1� Up

� � � f2 1� gp� �" #1

4

Ts ð22Þ

with T2 the temperature of the cosmic background radiation, which is as-sumed to be 0 K. Combining Eq. (22) with Eq. (15), which relates the averageplanet temperature Tp to the temperature of the Sun, we find that

T1 ¼ 214 � Tp ¼ 1:19Tp ð23Þ

and

g1 ¼ 2kR2pj 1� gp� � ð24Þ

with radiation conductancies

g1 ¼ g2 ð25ÞWe have now arrived at the so-called Stefan–Boltzmann engine. A blacksurface at temperature T1 emits energy at a rate

�Qin to a black surface at T3

Chapter 15220

that absorbs it. This is an irreversible process described by Eq. (20). Next, a re-versible engine operates between T3 and T4. Heat at a rate

�Qout is emitted by

the black body at T4 according to the irreversible process described by Eq.(21) where the cosmic background radiation has been neglected and thus T2

= 0 K. This is the setup of an endoreversible engine for which all ir-reversibilities are concentrated within the interaction of the engine with itsenvironment, with no irreversibilities taking place within the engine. We haveseen this before in Chapter 5 Section 2, the only difference being that in thelatter case heat was exchanged by conduction and convection rather thanradiation. The characteristics of this Stefan–Boltzmann engine are showngraphically in Fig. 3. As described earlier in Chapter 5, this engine also hasmaximum power performance. Given T1 = 21/4.Tp = 1.19 Tp and T2 = 0 K,numerical calculations show that T3 = 1.107 Tp and T4 = 0.767 Tp and thusthe efficiency D is given by

D ¼ 1� T4

T3¼ 0:307 ð26Þ

This efficiency refers to the engine and relates the net power output�W ¼

Q�in � �Qout to the heat input rate

�Qin:

D ¼�W�Qin

ð27Þ

In contrast to this engine efficiency, one defines the solar energy efficiency w as

w ¼�W�Qabs

ð28Þ

Figure 3 The Stefan–Boltzmann engine.

Solar Energy Conversion 221

The quantity�Qabs = kRp

2 (1 - U).fjT s4 is the total solar energy absorbed

by the planet per unit time. Calculations show that at maximum power,where D = 0.307, the efficiency w = 0.0767, or 7.67%. This value isindependent of f, U, and g and thus is the same for all planets, even thosein other solar systems since w is also independent of Ts.

Figure 4 shows a refinement on the model as proposed by De Vos andFlater [4]. They consider the ultimate fate of the wind power output

�W and

assume that an amount of heat equal to�W is absorbed within the planet’s

atmosphere. Defining a as the fraction of this heat that is absorbed at theilluminated side of the planet, they find that for

a ¼ 0 w ¼ 6:01%

a ¼ 0:5 w ¼ 6:90%

a ¼ 1:0 w ¼ 8:30%

It is interesting to note that in an experimental study of the limits to windpower utilization, Gustavson [5] found w = 3%.

3 PHOTOTHERMAL CONVERSION

In photothermal conversion, solar radiation energy is absorbed in a con-version device that drives a Carnot engine. The integrated device has beenmodeled by Muser [6] and has been named the Muser engine. The model is

Figure 4 Two models for the conversion of solar energy into wind energy. (a)

Preliminary model and (b) extended model.

Chapter 15222

depicted in Fig. 5. Radiation takes place from an effective sky temperature T1

(see below) toward a black body at temperature T3 that absorbs the radiationenergy. The Carnot engine, operating between T3 and T2, rejects heat to theenvironment at T2 = Tp, the planet’s temperature. This is another exampleof an endoreversible engine, where the irreversible part of the process is con-sidered to take place outside the engine, namely in the radiation exchange step.

The solar converter is positioned perpendicular to the sun’s rays andabsorbs per m2

�E ¼ fjT 4

s ð29Þin which f is the dilution factor of Eq. (10). In addition, the converter absorbsblack-body radiation from the environment at temperature Tp:

�E V ¼ 1� fð ÞjT 4

p ð30ÞFinally, the converter emits black-body radiation at temperature T3:

�E VV ¼ jT 4

3 ð31Þassuming that only the upper surface of the converter is an emitter and thatthe lower surface has a zero emissivity, that is by applying a certain coating.So the net incident energy flux is

�E net ¼ j fT 4

s þ 1� fð ÞT 4p � T 4

3

h ið32Þ

Defining the effective sky temperature T1 by

T 41 ¼ fT 4

s þ 1� fð ÞT 4p ð33Þ

we find T1 i 51/4 Tp = 1.50 Tp. So for Tp = 288 K, our planet’s effective skytemperature, T1 = 432 K. To establish the maximum power of the Muser

Figure 5 The Muser engine.

Solar Energy Conversion 223

engine, we determine the optimal temperature T3 of the solar converter. Forthis temperature it is found that the engine efficiency is D= 0.20 and that thesolar energy efficiency is

w ¼�W

fjT4s

¼ 0:13 ð34Þ

The concentration factor C has been defined as the factor by which theincident solar radiation can be augmented. The ideal concentrator wouldcompensate for the effect of the dilution factor f= 2.16 � 10�5, the value forour planet. The maximum concentration factor therefore is Cmax = 1/f =46,300. For an arbitrary value of C, Eq. (32) has to be adapted according to

�E net ¼ j CfT 4

s þ 1� Cfð ÞT 4p � T 4

3

h ið35Þ

Applying the same procedure for determining themaximum power character-istics as before and assuming moderately concentrated sunlight for which C= 389 [1], the solar energy efficiency w increases from 13% to somewhatabove 60%. For the limit case ofC=Cmax—all solar radiation is captured byour planet—w is close to 85%.

Another way to improve on the solar energy efficiency w is to applyselective coating on the converter’s absorbing and emitting surface. Thesecoatings oppress the radiation emitted by the converter without affecting theabsorption of the solar radiation. This effect can be achieved because thePlanck spectra at Ts, the temperature of the sun, and T3, the temperature ofthe converter, are more or less positioned next to each other as can be seenfrom Fig. 2. This is only true if T3b Ts and thus if the concentration factorCis not too high. The effect of these so-called bandgap materials can be im-pressive. Without concentrators, that is, for C = 1, w = 13% without ap-plying these materials. Introducing these materials can enhance w up to 54%.With a moderate concentrator, C = 389; this value can even be increased tow = 70%. This should conclude the main features of photothermal conver-sion.

4 PHOTOVOLTAIC ENERGY CONVERSION

Whereas in photothermal energy conversion radiation creates a temperaturedifference that is the origin for driving a heat engine, in photovoltaic energyconversion radiation creates a potential difference that can generate anelectric current. Such devices make use of very special materials, calledsemiconductors. Under certain circumstances a semiconductor can prevailin two states of matter. Within such states electrons can occupy a range of

Chapter 15224

energy levels; such a range is often named a band. Energy levels between suchbands cannot be occupied. The minimum distance between such bands iscalled a gap,Eg, and this is amaterial constant. Incident radiationmay initiatea transition of an electron from an energy level within one band (e.g.,E1) to anenergy level within the other band (e.g., E2), and thus the correspondingphoton frequency A is given by

E2 � E1 ¼ hv ð36ÞObviously E2�E1 should be larger than Eg. The energy of electrons within thetwo bands called the conduction band c and the valence band v refer todifferent Fermi energies EF. The distance in Fermi energies EFc and EFv is

EFc � EFv ¼ qV ð37Þin which q is the unit of electrical charge and V the generated potentialdifference. By tuning the potential difference, the device can emit a certainradiation spectrum; by varying the incident radiation, the device can generatevarious electrical currents. In this instance it is important to concentrate onthe electron flux

�N, just as we did on the heat flux

�Q in photothermal energy

conversion. We distinguish between electron fluxes associated with photonsabsorbed from solar radiation and with photons emitted from the absorbingmaterial. The associated electric current is given by

I ¼ q�N ð38Þ

The associated electric voltage V is given by Eq. (37) and thus the electricpower is given by

�W ¼ VI ð39Þ

The solar energy efficiency w, as defined before by

w ¼�Wout�

Qsolar;absorbed

ð40Þ

can now be calculated and its maximum value established. It is found that formaximum power w = 31% for nonconcentrated sunlight (i.e., for C = 1) atan optimal bandgap E opt

g = 1.30 eV. For moderately concentrated sunlight,with C = 389, w rises to 35% for E opt

g = 1.10 eV. In reality, however, it isdifficult to attain values for w larger than 13%.

It has been found that hybrid energy conversion may lead to bettervalues for w than either from photovoltaic or from photothermal conversion.In hybrid conversion, solar cells mounted in roof panels, for example, providethe electricity whereas heat is extracted from the panels to possibly drive heatengines. Although theoretical calculations show significant improvements for

Solar Energy Conversion 225

a hybrid photothermal solar energy convertor, values of w of nearly 70%compared to those of 50% for photothermal and 30% for photovoltaicconversion for nonconcentrated sunlight, this application has not reached yetthe practical stage other than using the liberated heat directly instead of in aheat engine.

Finally, we briefly discuss what is called multicolor and omnicolorconversion. Instead of using a single solid-state material with one bandgapEg as characteristic material property, one can select two or more materials,each with its own bandgap. In such systems, according to De Vos, eachmaterial is responsible for the conversion of a particular energy band of theincoming solar radiation. Because each band of the light spectrum can becharacterized by a particular ‘‘color,’’ one speaks of multicolor conversion.Multicolor conversion can refer to photothermal and photovoltaic energyconversion and their hybrid applications. De Vos deals with the nonhybridcases in his book and shows that for an infinite number of colors, when wespeak of omnicolor conversion, the distinction between the two conversionmethods disappears and reaches, for nonconcentrated sunlight (i.e., C = 1),the thermodynamic limit for solar energy conversion efficiency w of 68.2%.For fully concentrated sunlight, C = 1/f, w = 86.8%. This then can beconsidered to be the exergy for sunlight for this way of converting sunlight byabsorption. When sunlight is used as a heat source at Ts in a heat engine, theexergy reaches the absolute limit of 0.95, which is the Carnot factor betweenTs = 5762 K and Tp= 288 K. For a discussion on the exergy of radiation, werefer to Petela [7].

5 PHOTOSYNTHESIS

The unforgettable Albert Lehninger [8], who in his teaching of biochemistrymade extensive use of thermodynamics, called light energy the ultimate sourceof all biological energy. It is absorbed by photosynthetic cells in the form ofchemical energy that is then used to convert carbon dioxide into glucose. Thisreaction is usually given by the equation

6CO2 þ 6H2O! C6H12O6 þ 6O2 ð41ÞWriting this equation in the simplified form

CO2 þH2O! CH2OþO2 ð42Þand using exergy values for reactants and products, we conclude that thisreaction requires roughly 480 kJ per mole of CH2O, an elementary glucoseunit, as input of work. This work is furnished by light.Water acts as the donor

Chapter 15226

of hydrogen and electrons, whereas CO2 acts as their acceptor, which isexemplified by the redox reactions

2H2O! 4Hþ þ 4e� þO2 ð43ÞCO2 þ 4Hþ þ 4e� ! CH2OþH2O ð44Þ

The two oxygen atoms in the liberated oxygen molecule O2 do not stem fromCO2 but from water, and therefore Eq. (42) is too simple and should bewritten as

CO2 þ 2H2O*! CH2OþO*2 þH2O ð45Þand Eq. (41) should read

6CO2 þ 12H2O*! C6H12O6 þ 6O*2 þ 6H2O ð46ÞThe asterisk emphasizes that the liberated oxygen originates from reactantwater and that carbon dioxide’s oxygen is distributed evenly over glucose andproduct water. Equation (44) is representative for how higher plants trans-form the energy of light into chemical energy. However, purple bacteriaabsorb light by the simplified reaction

CO2 þ 2H2S! CH2Oþ 2SþH2O ð47ÞUsing exergy values for reactants and products, this reaction needs only 76 kJper mole of CH2O. These bacteria may also absorb light by means of thereaction

CO2 þ 2H2 ! CH2OþH2O ð48Þand this reaction needs only about 20 kJ of exergy input per mole of theelementary carbohydrate unit. These simple calculations suggest that purplebacteria can deal with scarce light sources, although they have preparedthemselves for this by the preliminary synthesis of H2S and H2, respectively.

Another interesting aspect of photosynthesis by higher plants is thedistinction between so-called light and dark reactions. The light reactionsabsorb light and convert this into chemical energy; the dark reactions convertcarbon dioxide into glucose with chemical energy but without light. In thelight reaction, chlorophyl plays an important role in the capture of the energyof light by rearrangement of electrons in its molecules. In the transport ofelectrons, NADP, or nicotin amide adenine dinucleotide phosphate, plays acrucial role in the transport of the absorbed energy as chemical energy, theearlier mentionedATP or adenosine triphosphate, is essential (see Chapter 4).To bring these two molecules NADP and ATP in proper position for thesynthesis of glucose from CO2, another reaction is required that overallgenerates oxygenwhile absorbing light. It is interesting to observe that oxygen

Solar Energy Conversion 227

liberation and carbon dioxide conversion take place in completely differentreactions, not in the same reaction although this is suggested by Eq. (41) or(46).

A final word about the thermodynamic efficiency of photosynthesis. DeVos reports in his book solar energy conversion on the order of 2–2.5% forland plants such as crop, rice, and wheat and values as high as 18% for seaplants such as algae. But he cautions that these results were obtained by agri-cultural engineers and biologists who tend to take into account only the visiblepart of solar energy as the input energy. De Vos [1] then shows that a correc-tion factor of 0.368 is required, thus reducing the values to 0.8% and 6.6% forland and sea plants, respectively. In passing, he mentions that 0.1% (!) of thesolar flux incident on the earth is converted to chemical energy by photosyn-thesis, which is an impressive figure indeed.

These thermodynamic efficiencies may be considered to be on the lowside, particularly for land plants. But then it must be noted that thisphotosynthesis is an activity of a living system for which photosynthesis, orrather the capture of solar energy and its transformation into chemicalenergy, is only one aspect of life. Supply may exceed demand. Therefore, itmay well be that if the purpose of photosynthesis is only the capture of light asan energy source, the efficiencies would have been higher. Support for thisconjecture can be found in a calculation by Lehninger [8], who shows thatunder certain laboratory conditions efficiencies can rise to 36% for greenalgae or even isolated chloroplasts. Perhaps even higher efficiencies arepossible for nonliving systems for the production of exergy carriers.

6 CONCLUDING REMARKS

The sun is an abundant albeit dilute source of energy. Some call it the world’smost distant and safest nuclear reactor [9]. By the time solar radiation reachesthe earth’s outer atmosphere, its intensity has been reduced by a factor f =2.16� 10�5 due to the earth’s distance to the sun. The so-called solar constantS= 1353 W/m2 is the corresponding flux. A more practical value is Z= 947W/m2 in which Z= (1 � U)S. U is the earth’s albedo, accounting for the factthat not all solar radiation that reaches the outer atmosphere is absorbed.Solar energy can be naturally converted into wind energy or biomass withoutthe intervention of man. This in contrast to the conversion into heat for thegeneration of work or into electricity as in photovoltaic energy conversion.The efficiency of these conversions is best expressed in terms of the so-calledsolar energy efficiency w, which quantifies the maximum amount of work thatunder practical conditions, including irreversibilities, can be extracted fromthe solar energy absorbed by the planet, which is related to Z. In this way one

Chapter 15228

can calculate for wind energy that the best value to be attained is w= 0.08 or8%, but in practice a value of 3% seems to be more realistic.

In photothermal conversion, the best value possible seems to be w =0.13. However, by making use of ingenious devices for refraction andreflection, the intensity of captured solar radiation can be enhanced by aconcentration factorC close to 400.w can then reach values close tow=0.60.Another way to enhance w is to apply so-called bandgap materials thatsuppress the emission of absorbed solar energy by capturing this energy withthe help of electronic rearrangements in the material. The material ischaracterized by the so-called bandgap in eV. For nonconcentrated solarradiation, C=1, w can be calculated to reach a value of 0.54, or 54%, for anoptimal bandgap ofEg= 0.90 eV. For concentrated sunlight atC=400,w=0.70 for a somewhat lower value of Eg = 0.70 eV.

Photovoltaic energy conversion also makes use of bandgapmaterials forthe direct conversion of radiation energy into work, electricity. ForC=1, thebest value for w = 0.31, or 31%, at an optimal bandgap Eg = 1.30 eV withw=25% reached in the laboratory and 15% in industrial production. For C= 400, w increases to 35%. For multicolor conversion where many differentbandgapmaterials are applied simultaneously,w can be calculated to increasesignificantly, namely to values in the order of 70–80%. In practice, however, itis difficult to realize values higher than 35%.

Table 1 Summary of Solar Energy Conversion Technologies

Conversion technology w (%)

Wind energy theoretical 6–8.5experimental 3

Photothermal C = 1 13

C = moderate f60C = maximum 85

Photothermal with bandgap material C = 1 54

C = moderate 70Photovoltaic C = 1 31

C = moderate 35in practice 15

Hybrid theoretical 70Multicolor C = 1 68

C = maximum 87

Photosynthesis land plants 0.8sea plants 6.6experiment 36

Solar Energy Conversion 229

In photosynthesis, absorbed solar radiation is captured as chemicalenergy. In this spontaneous natural conversion of absorbed solar radiation,the solar energy efficiency w ranges from 0.8% for land plants to 6.6% for seaplants. In laboratory experiments efficiencies above 30% have been observed.

Table 1 summarizes the results of solar energy conversion, as discussedin this chapter.

Solar energy is a truly sustainable and ample source of energy, and itsconversion still poses many challenges. Overcoming these challenges willfacilitate the transformation of our society into a sustainable one. It should beclear that there is a great deal of scope for research in the field of solar energyconversion. Practical photovoltaic energy conversions, for example, still fallshort of the theoretical limit. To the best of our knowledge, hybrid andmulticolor conversions have not reached an experimental stage even thoughtheoretical conversions are very high. Clearly, the potential benefits of thesetechnologies are great. Advances in the field of biotechnology may enable theuse of photosynthesis for the production of specialty chemicals at highefficiency.

REFERENCES

1. De Vos, A. Endoreversible Thermodynamics of Solar Energy Conversion; OxfordUniversity Press: Oxford, 1992.

2. Thekaekara, M. Solar energy outside the Earth’s atmosphere. Solar Energy 1993,

14, 109–127.3. Gordon, J.; Zarmi, Y. Wind energy as a solar-driven heat engine: A thermo-

dynamic approach. American Journal of Physics 1989, 57, 995–998.

4. De Vos, A.; Flater, G. The maximum efficiency of the conversion of solar energyinto wind energy. American Journal of Physics 1991, 59, 751–754.

5. Gustavson, M. Limits to windpower utilization. Science 1979, 204, 13–17.

6. Muser, H. Behandlung von Elektronenprozessen in Halbleiter Randschichten.Zeitschrift fur Physik 1957, 148, 380–390.

7. Petela, R. Exergy of heat radiation. Journal of Heat Transfer,May 1964, 187–192.8. Lehninger, A.L. Bio-energetics, 2nd ed.; W.I. Benjamin: Menlo Park, CA, 1973.

9. Okkerse, C.; van Bekkum, H. Towards a plant based-economy? In Starch 96—The Book, Carbohydrate Research Foundation; The Hague: The Netherlands,1997.

Chapter 15230

16Biomass Production and Conversion

In this chapter we will discuss biomass as a source for the chemical and energyindustries. Typical sources are outlined, and a survey of existing biomass con-version technologies is presented.

1 INTRODUCTION

Biomass is among the oldest resources known to man and an important con-tributor to the world economy [1]. Biomass comprises any organic matter—wood, plants, crops, and animal waste are good examples. It is both an energyresource and a raw material. The burning of wood for purposes of heat andlight has been commonplace for millennia, and early fabrics were comprisedentirely from biomass. Indeed, even today, cotton and wool are still popu-lar materials in the clothing industry. Recently, a true revolution in the lifesciences has begun. This revolution has the potential to radically change thegreen plants and products we obtain from them. Green plants developed toproduce desired products and energy could be possible in the future.

Accordingly, biomass has become increasingly popular again. The reas-ons are simple. Biomass is, per definition, renewable and sustainable if theamount utilized equals the amount that is naturally replenished, for instanceby replanting in the case of wood utilization. Broadly speaking, biomass canbe utilized as (1) a source of renewable chemicals andmaterials or (2) an ener-gy source. In this classification, we use materials in the broad sense, andbiomass as information carrier falls under that distinction.

Now, biomass is a ‘‘substance,’’ if you may, which consists of primarilycarbon, hydrogen, nitrogen, and oxygen and has a complicated chemicalstructure. It can be a source of chemicals or materials by minor modificationof the biomass (e.g., cotton, wood). For a substantial review of renewablematerials, we refer to the references of that chapter. Substantial modificationof the biomass yields products that are sources of carbon and hydrogen. This

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can be achieved by gasification, yielding carbonmonoxide and hydrogen, alsoreferred to as synthesis gas; by hydrothermal upgrading yielding an oilysubstance that has been termed bio-crude oil; or by other technologies. Thesynthesis gas or bio-crude can then be subjected to processing steps similarto those used in the traditional petrochemical industry to yield valuableproducts.

When viewing biomass as an energy carrier, one can convert the bio-mass into a fuel by a number of conversion technologies such as hydrothermalupgrading toward bio-crude, bacterial decay yielding methane, or one mayelect for direct combustion.

It is not hard to understandwhy biomass is of interest as a source of bothchemicals and energy. Biomass is a renewable resource, and the amounttherefore constitutes an effectively infinite source of rawmaterial if the rate ofconsumption is equal to the rate of biomass regeneration or growth. The use ofbiomasshas certain restrictions, ofwhich three importantonesare: (1)biomassshould be used in such a way that biodiversity is preserved; (2) the quality ofbiomass varies from source to source; and (3) use of land for biomass cul-tivation competes with the use of the land for food cultivation. Furthermore,when viewing biomass as an energy source, any CO2 emission is counter-balanced by the amount of CO2 used during growth. Biomass combustion isseen as a means of closing the carbon cycle, as, in effect, solar energy is con-verted to chemical energy via photosynthesis and ultimately thermal energy.

It is natural to wonder why combustion of biomass is an example ofsustainable technology, as combustion releases carbon dioxide in the atmo-sphere and therefore does not seem to close the material cycles. While thecombustion does release carbon dioxide into the atmosphere, the growth ofbiomass consumed carbon dioxide (see Fig. 1). Therefore, the final result is

Figure 1 Schematic of generation and use of biomass illustrating closed elementalcycles.

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that there is no net release or consumption of carbon dioxide if the biomass isreplenished. Consider the example that a certain unit of active biomassabsorbs one unit of carbon dioxide per unit time while growing. If one unitof this biomass is combusted, thus releasing one unit of carbon dioxide, theresult is that there is no net increase or decrease in carbon dioxide emission.The analogous argument holds for the other materials used during growth ofthe biomass such as minerals. Note that the minerals are transformed to ashduring combustion which is a form that cannot be readily assimilated duringgrowth. The whole process is sustainable provided the use of one unit ofbiomass is counterbalanced by the replenishment of biomass by growth.However, it is important to note that with the current state of technology, useof fossil fuels is inevitable in various process steps and the complete processmay not be entirely renewable; a closer look at these processes is necessary todetermine their renewability. Finally, we note that the depletion of forestlands is not an example of sustainable technology since there is no refores-tation to balance the consumption. The recycling of minerals, e.g., N, S, P,and K, is also important to replenish the soil.

In this chapter, we examine some common sources of biomass in Section2, followed by a discussion of conversion technologies in Section 3. Someconcluding remarks are made in Section 4.

2 BIOMASS SOURCES

Asmentioned earlier, any organicmatter can be considered biomass. Biomassacts as a carbon dioxide sequestering agent by using the carbon dioxide duringphotosynthesis. In this process, the energy of the sun is stored in chemicalform (see Fig. 1). In a sense, therefore, the sun is the ultimate source of energy,and the biomass is the intermediate. All plants are examples of biomass. Plantand yard cuttings are also biomass, as is wood waste such as saw dust.Agricultural residues such as bagasse from sugarcane, corn fiber, rice strawand hulls, and nutshells are also considered biomass. Now, paper trash is alsobiomass since it ultimately was made fromwood, and a lot of municipal wasteis also biomass [2]. It is convenient to further classify the biomass based onfunction. We choose to consider biomass that is cultivated to serve as abiomass source as dedicated or primary source, and consider biomass residuesuch as woodwaste a secondary source or biowaste. Primary biomass iscultivated with a specific purpose in mind, and the conversion technologiesthat use this biomass are dedicated conversion plants. For example, sugarcaneis grown for the purpose of producing sugar and is therefore a primary source.The residues of the sugarcane processing are biowaste and can be either pro-cessed separately or mixed up with other biowaste and therefore deemed asecondary source.

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When classifying biomass for purposes of generating energy, it is com-mon to do this based on its source. The following classification is generallyused [3]:

1. Woody biomass. As mentioned earlier, wood is the oldest biofuel.Conventionally, wood would be harvested from forests by simple logging.This conventionalmethod does not replenish the harvested wood and is there-fore not sustainable. The current paradigm is to grow wood specifically forpurposes of harvesting by means of short-rotation forestry.

2. Energy crops. Energy crops are simply crops grown for this specificpurpose and are continually replanted once harvested.Woody short-rotationcrops are examples of these crops. Trees such as the poplar, eucalyptus,willow, and conifers are expected to be useful [3–9], as are agricultural cropssuch as the sweet sorgum and algae.

3. Residues. Residues from the forest such as twigs, from the agricul-tural industry, from wood processing (wood dust), as well as from animalfarming (manure) are good examples of residue biomass.

4. Municipal waste. Municipal waste contains large amounts of bio-mass. Use of biowaste as a source transforms a negative-value substance,namely the waste, into saleable products such as energy and/or compost [4]. Itis therefore useful in reducing waste, and providing fully renewable energy,since biological waste will be available. The United States alone generatedaround 208 million tons* of municipal solid waste in 1995 [5]. The wasteconsisted of 66.7% biomass (paper and paperboard, yard trimmings, food,and wood), the remainder being made up by nonbiomass items such as glass,plastics, andmetals. The breakdown in other countries seems to be similar [6].

As mentioned earlier under the heading of residue, manure is a goodbiomass source, and there is certainly no shortage of that. The estimatedannual U.S. manure generation as a byproduct of farming in 1997 in dryweight units is as follows [10]: cattle, 118,424,288 tons; poultry, 17,859,625;swine, 9,341,288. Others estimate the manure production by cows alone to beapproximately 1 billion tons [11]. We can estimate the exergetic value of themanure by examining the caloric values of the dry manure, which we considerto be fuel (see Chapter 9). The caloric value ofmanure depends strongly on thetype of cow and ranges between 16,771 kJ/kg for fresh beeflot manurey to10,607 kJ/kg for dairy cow manure [12–15]. For purposes of obtaining anorder-of-magnitude estimate, we will simply use the mean of these twonumbers: 13,689 kJ/kg. The production of cattle manure is between 0.1 and1 billion tons, or 0.1� 2000/2.2= 91� 109 kg and 1� 2000/2.2= 910� 109

*1 ton =2000 lb, 1 tonne =1000 kg.yWe have used the average of the lower and higher heating values to obtain these figure.

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kg. We note, however, that based on the estimates of manure generation inThe Netherlands (shown later), the larger number is more likely to beaccurate. The approximate exergetic* value of the cattle manure is thereforebetween 91� 109� 13,689� 103 = 1.2� 1018 J and 1.2 � 1019 J. To put thisfigure in perspective, we compare this to the electricity demand in the UnitedStates in 2001, which was 1.3 � 1019 J and the exergetic value of the oilconsumption,y which was 19.7 million barrels a day, or 19.7 � 106 � 365 �6105.6� 106 J/bbl =4.4� 1019 J [16]. The numbers suggest that the exergeticvalue of the manure, which is a waste product, is comparable in order ofmagnitude to the electricity demand and exergetic value of the oil consump-tion. A similar calculation can be made for The Netherlands. In The Nether-lands in 1986, 1011 kg of manure was produced [17]. Using the same methoddescribed earlier, this is equivalent to 1011 � 13,689 � 103 = 1.4 � 1018 J.Compare this to the total energy consumption of The Netherlands in 2001,whichwas 4.1� 1018 J, and it is clear that these numbers are of similar order ofmagnitude [18]. Clearly, the use of biomass as a source for energy productionis not hampered by the lack of it!

The use of crops for the purpose of generation of energy has beendescribed in the literature [3–9,19]. The use of energy crops reduces the netcarbon dioxide emissions by a significant amount. More information oncarbon dioxide emissions can be found in the literature [20]. Typically, cropsused for these fuel purposes include short-rotation woody crops and short-rotation herbaceous crops such as switch grass [22].

3 CONVERSION TECHNOLOGIES

The following conversion technologies are recognized to convert biomass toenergy:

1. Combustion2. Pyrolysis3. Gasification4. Upgrading by chemical or biochemical means

Combustion is by far the oldest method of utilizing biomass and has tra-ditionally involved the burning of wood, dung, and other materials.z The

*Since we consider manure as fuel, we estimate the exergetic value by using the caloric value.yThe chemical exergy of crude oil is approximately 6105.6 MJ/bbl [21].zAlthough combustion of biomass in households is still prevalent in certain countries, we will

not discuss this but will focus on larger-scale technological processes.

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other methods are, comparatively speaking, more recent. In this section wewill outline these methods.

3.1 Combustion

Conceptually speaking, the technology for combustors is similar to that usedfor coal combustion (see Chapter 9) if solid biomass fuels are used. Typicallyused configurations for biomass combustion include [23] (1) pile burned, (2)stoker fired, (3) suspension fired, and (4) fluidized bed combustors.

As the name suggests, in pile burners the biomass is arranged in pile-likefashion in a furnace and burned. The combustion air comes from above andbelow the pile. Advantages of this technology include the flexibility in choiceof fuel and the simple design. However, boiler efficiencies are generally lowerthan those of the other technologies, and with poor control over thecombustion process these are drawbacks of this technology.

A characteristic of the stoker fired boilers is that there is a fuel feedingsystem that puts a thin and evenlydistributed layer of fuel onagrate,which canbe sloping, traveling, or vibrating.The layerof fuel on the grate ismuch thinnerand more evenly distributed than in the case of the pile burners. In thestationary sloping grate boiler configuration, the grate does not move andthe fuel burns as it slides down. Since the feed rate of fuel is controlled bygravity, the riskof feeding toomuch inanavalanche is real, and thecombustionprocess is more difficult to control. In the traveling grate boiler, the fuel is fedon one side of the grate, it is burned, and the ash is transported to the dumpingsite of the furnace. Combustion control is improved in this configuration. Thelayer of fuel is thinner than that encountered in the sloping grate, and as aresult the carbonburnout rates arebetter.Withavibratinggrateboiler, the fuelis fed evenly on the whole grate. The vibrating grate spreads the fuel evenlydue to its shaking motion. The maintenance requirements are lower for thistype of grate, since the number ofmoving parts is less than that of the travelinggrate. Carbon burnout efficiency is further improved in this configuration.

The suspension fired boilers are similar to the pulverized coal firingtechnology and involve combusting the fuel in the form of small particles asthey are fed into the boiler. A great deal of pretreatment is required of the fuel,which is a potential disadvantage. However, the higher boiler efficiency is anadvantage.

Fluidized bed systems combust the fuel, which has been fluidized byhigh-velocity air. In general, fluidized bed systems are flexible in terms of fuelrequirements. As a result, they are quite suitable for simultaneous combustionof biomass and other fuels. The carbon burnout efficiency is quite high influidized beds. The possibility to control creation of harmful oxides of nitro-gen (NOx) and sulfur (SOx) make fluidized beds an attractive option.

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Biomass differs from conventional fossil fuels in the variability of fuelcharacteristics, higher moisture contents, and low nitrogen and sulfur con-tents of biomass fuels. The moisture content of biomass has a large influenceon the combusion process and on the resulting efficiencies due to the lowercombustion temperatures. It has been estimated that the adiabatic flametemperature of green wood is approximately 1000jC, while it is 1350jC fordry wood [23]. NOx formation in biomass combustion can be kept low, partlybecause of low nitrogen contents in most biomass fuels and partly with thehelp of control techniques like combustion at low temperatures and stagedcombustion [23]. The chemical exergies for wood depend heavily on the typeof wood used, but certain estimates can be obtained in the literature [21]. Forexample, for wood consisting of 42.6 wt% carbon, 5.2 wt% hydrogen, 36.6wt%oxygen, 0.1 wt%nitrogen, 15 wt%water, and 0.5 wt% ash, the chemicalexergy is 17,641 kJ/kg [21]. The thermodynamic efficiency of wood combus-tors can then be computed using the methods described in Chapter 9. Typicalcombustion temperatures range from approximately 800jC for fluidized bedcombustors to 1300jC for pile burners [23–25]. Based on an extensive surveyof some existing biomass conversion plants, it seems that the maximum steamtemperature was around 540jC [23]. Reported net electrical efficiencies basedon the lower heating value of the biomass (that is, the number of Joules ofelectricity per Joule of biomass) were between 20% and 40% [23]. It seemsthat the newer biomass conversion plants have higher efficiencies, primarilydue to higher boiler and turbine efficiencies. Note that existing combinedcycles that use fossil fuels have efficiencies of around 50%, so the efficiencies ofthe biomass conversion plants are reasonable (see Chapter 9).

Now, while the combustion of biomass typically requires modificationsto coal combustors, simultaneous combustion of coal and biomass, alsoreferred to as co-firing, in coal combustors requires very little, if any, mod-ification to the combustors [26]. Biomass co-firing within the existing infra-structure of pulverized coal utility boilers is viewed as a practical means ofencouraging the use of renewable energy while minimizing capital cost re-quirements and maintaining the high efficiencies of pc boilers. The wide dis-persion of pulverized coal boilers (in number and capacity) translates intosignificant potential opportunities for biomass utilization [27].

Co-firing is an extension of fuel blending practices common to the solidfuels community. A number of power companies [28] have developed a con-certed effort to commercialize direct combustion co-firing of biomass withcoal. In the United States and Europe, co-firing programs have been extensiveand are now ready for commercial deployment [28].

The use of wood to reduce NOx is attractive for several reasons. First,wood contains little nitrogen as compared with coal, which is also used as areburning fuel. This results in lower NOx production from fuel nitrogen

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species for wood. In addition, wood contains virtually no sulfur, so sulfurdioxide (SO2) emissions are reduced in direct proportion to the coal replace-ment. Experimental results showed dramatic NOx reductions with approxi-mately 10–15% wood heat input. Computer modeling of a cyclone-firedboiler has shown that NOx reductions as high as 50–60% could be achievedwithin the constraints set by the boiler and operations. The combination ofcomputer simulations and experimental programs has provided the engineerswith the tools needed to optimize biomass as a reburn fuel to maximize NOx

reduction [29].We note in passing that countries with large deposits of coal are unlikely

to switch to biomass-only combustion and are likely to opt for co-firinginstead. The operating temperature is partly determined by the compositionof the ash forming compounds present in the biomass.

3.2 Pyrolysis

Pyrolysis is the degradation of macromolecular materials with heat alone inthe absence of oxygen [30]. The development of pyrolysis processes for liquidsproduction has gained much attention in the last decade because they offer aconvenient way to convert low-value woody residues into liquid fuels andvalue-added products. Biomass pyrolysis is of growing interest as the liquidproduct can be stored and easily transported. [31]. Pyrolysis processes yield amixture of gas, liquid, and solid products. If pyrolysis is practiced alone, thatis, without a subsequent gasification step (see the next section), the processconditions are usually chosen to maximize liquid product yields.

The body of literature describing biomass pyrolysis is large, and we giveonly a brief overview of some of the commonly used pyrolysis technologies[32–34]. The conditions under which pyrolysis processes are operated range agreat deal. In general, the operating temperature is between 400jC to 1000jC.Different pyrolysis processes [32] include (1) entrained-flow pyrolysis, (2)vacuum pyrolysis, (3) fast pyrolysis, (4) rapid thermal pyrolysis, (5) vertexablative pyrolysis, (6) fluidized bed pyrolysis, (7) pyrolysis with partialcombustion, (8) low-temperature pyrolysis, and (9) updraft fixed bed pyrol-ysis. A full discussion of the different pyrolysis processes is beyond the scopeof this chapter, but we will touch on the first two.

In entrained-flow pyrolysis [32,35,36], the wood, which has beenreduced in size to less than a millimeter,* is entrained in by hot gases, whichsupply the heat for the pyrolysis. In order to maximize the yield of pyrolysisoil, a gas-to-biomass ratio of about 8 is used. The process takes place around

*It is important to realize that reducing solids in size is an energy-consuming exercise!

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745jC. The process yields 58% organic condensates, 12% char, and 30%other components by weight.

In vacuum pyrolysis [32,37,40] the biomass is pyrolyzed under vacuumin staged multiple-hearth furnaces at temperatures between 350jC and450jC. The liquid product fractions are collected from each stage of thefurnace. Feeds that have been studied include wood chips, bark, agriculturalresidue, peat, and municipal solid waste.

The process conditions are important in determining the productbreakup and liquid yield. If the purpose is to maximize the yield of liquidproducts, a low-temperature, high-heating-rate, short gas residence-timeprocess would be required. For high-char production, a low-temperature,low-heating-rate process would be chosen. If the purpose is to maximize theyield of fuel gas resulting from pyrolysis, a high-temperature, low-heating-rate, long gas residence-time process would be preferred [41].

3.3 Gasification

Biomass gasification involves the transformation of biomass into a mixtureof carbon monoxide and hydrogen, also referred to as synthesis gas, and car-bon dioxide. These chemicals can then be transformed to a variety of chemi-cals using Fischer–Tropsch synthesis or biochemical means to fuels such asethanol [42], or used as feed for fuel cells, turbines, and so on to generateelectricity. The technology is therefore very attractive given the flexibility inuse of the products. Gasification provides a fuel that can easily be incorpo-rated into the existing infrastructure, and it allows for easy removal of com-ponents that cause problems for downstream power generation. Moreover,the technology allows the processing of many biomass wastes that cannotbe combusted.

Gasification consists of two endothermic steps, namely (1) pyrolysis,where volatile components in the biomass are vaporized, and (2) charconversion, which involves reacting the char with steam. The technology isanalogous to that used for coal. The pyrolysis step is more important in thecase of biomass than it is for coal since the content of volatiles is higher (70–86% on a dry basis compared to the 30% of coal). The heat requirements aregenerally supplied by combusting part of the char. A simple schematic is givenin Fig. 2.

3.4 Upgrading Biomass

The upgrading of biomass either by fermentation or by direct liquefaction hasbeen the topic of research for many years. It has been known for decades thatlandfills produce gas by bacterial decay (anaerobic fermentation) of the

Biomass Production and Conversion 239

biological constituents of the waste. This landfill gas consists mainly ofmethane and carbon dioxide. In the late 1970s landfill gas was first used asa fuel in the United States, and since then the technology to collect and use ithas improved gradually. This method of producing energy is now regarded asone of themostmature and successful in the field of renewable power. It is wellknown that methane is a more potent greenhouse gas than carbon dioxide,and its utilization as an energy source is therefore beneficial. The gas istypically around 50% carbon dioxide and 50% methane, though variation ispossible depending on the conditions.

Numerous landfills throughout the world produce gas used to generateelectricity [43,44], and additional increases in the landfill gas utilizationcapacity are expected [44,45]. As noted earlier, landfill gas technology is wellestablished. The gas is taken from the landfill through a series of wells andpiped to a processing station, where it is combusted to generate electricity. Atypical landfill has the potential to produce gas for 50 to 100 years [45,46]. Theproduction may only be economically feasible with current technology forabout 15 years. The yield of biogas can be increased by pretreating the wasteby steam pressure disruption [47] and can yield a net increase of power. Thesize of the generators at the landfill sites can be severalMW. For example, a 5-megawatt plant would produce approximately 42 million kilowatt-hours peryear—enough to supply about 3200 homes in the United States [46].

In Europe alone [47], approximately two thirds of the waste goes tolandfills, and therefore the waste constitutes a potential source of gas.However, bacterial decay as it occurs in the landfills has also been appliedto waste generated in farms [42]. The use of household and agricultural wasteto provide energy to distant rural communities is therefore believed to havepotential (e.g., [48,49]). In certain rural communities in China, for example,

Figure 2 Schematic representation of biomass gasification.

Chapter 16240

bacterial decay of biomass and sewage provides compost and biogas that aresubsequently used for soil quality improvement and heating and cookingpurposes [50,51]. Anaerobic fermentation of agricultural waste products suchas manure can yield valuable amounts of methane and compost.

Aerobic fermentation of pretreated biomass, on the other hand, canyield alcohols, which can be used as liquid fuels. This bioethanol is a usefulfossil fuel substitute [52]. It has been shown that the addition of ethanol togasoline reduces carbon monoxide emissions [52] and increases the octanerating in internal combustion engines. With current internal combustion en-gine technology, however, the mileage does reduce somewhat, but efforts areunderway to use the characteristics of the fuel to obtain higher mileage [52].

A recent economic analysis that examined all phases of ethanol pro-duction concluded that ethanol made from corn outperformed gasoline byusing less energy and producing fewer greenhouse gases [52–55]. When otherbiomass feedstocks are considered—such as hybrid poplars and switchgrass,which require little energy to grow and harvest—the benefits were evengreater. According to a fuel cycle evaluation conducted by the U.S. Depart-ment of Energy, the fuel cycle of ethanol produced from biomass feedstocksgenerates 6.8 Btu for every Btu of fossil energy consumed. The production ofreformulated gasoline, which is used in many urban areas of our country,generates only 0.79 Btu of fuel energy for every Btu of fossil energy consumed[52,54,55].

Some estimates are that by utilizing the full range of cellulosic biomassavailable, the entire U.S. demand for gasoline could be substituted by ethanol[56]. A large proportion of cars in Brazil uses pure ethanol (40%), while eth-anol/gasoline blends are also popular (22%) [56].

Bioethanol is suitable for internal combustion engines that run ongasoline. Similarly, biodiesel is designed for diesel engines. Biodiesel is a fuelmanufactured from various oils and fats. These acids are chemically trans-formed to fatty acid methyl esters. By blending the fatty acid methyl or ethylesters in the right proportions, the properties of the fuel can be influenced [57]and mimic the properties of petrochemically derived diesel. Biofuel efficiencygenerally is the same as for fossil-derived diesel fuel [57].

A large body of literature exists describing liquefaction processes (seefor a review, e.g., [32]). The hydrothermal upgrading process is a promisingliquefaction process [58,59]. The process involves treating the biomass byliquid water at temperatures ranging from 300jC–350jCat pressures between100 and 180 bar, and depolymerizing it to a hydrophobic liquid product,gaseous CO2, and water. A great deal of the oxygen leaves the biomass in theform of CO2. The resulting liquid is referred to as bio-crude oil. The bio-crudeoil is then sent to various upgrading processes, similar to the processing ofcrude oil.

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The exergetic efficiency of the HTU process has been reported in theliterature [60]. Depending on process conditions, the maximum exergeticefficiency can be as high as 86%, and on first sight can be energy self-sufficient,not requiring any additional fuel/energy input. This implies that the processcan be fully sustainable as well in terms of emissions of carbon, nitrogen,sulfur and so forth, since the raw material is renewable, consumes the sameamount of carbon, nitrogen, and sulfur during regeneration of biomass, and iscapable of supplying the energy demands of the process. However, if the elec-tricity demands, the hydrogen production for hydrogen treatment, the heatingrequirements and waste water treatment are taken into account, the efficiencydrops to 40% [61].

4 CONCLUDING REMARKS

It is clear from the overview given in this chapter that there is no shortage ofbiomass conversion processes. It also seems that there is an ample source ofbiomass as well. The sources of biomass are widespread and include woodycrops,manure, andmunicipal waste. Various processes exist to use biomass asa source of materials, chemicals, and energy. Use of biomass for eithermaterials, chemicals, or energy is sustainable provided the utilized biomassis replenished. More specifically, if crops are used as a biomass source, thesustainable process would entail replanting at the rate of use. However, acaveat is that nonrenewables are still necessary in the whole process, and thismust be acknowledged and addressed. In certain cases this can mean that aprocess that at first sight seems completely sustainable actually is not when allthe fossil-based fuel input is taken into account.

Biomass combustion offers promise for a sustainable method of heat-ing, and co-firing of biomass with fossil fuels can be implemented to reducecarbon dioxide emissions and requires little adaptation to existing fossil fuelcombustors. It is likely to be used in countries with large reserves of fossil fuels.

Biomass pyrolysis and liquefaction yield liquid products that can beused in processing facilities similar to those used for the petrochemical in-dustry to produce valuable products.

The gasification of biomass allows the synthesis of chemicals throughFischer-Tropsch technology and can also be used to produce synthetic liquidfuels, in a fully renewable fashion.

The anaerobic decay of biomass has the potential to transform agricul-tural and municipal waste into gas, which can be used to generate electricity.The technology is quitemature andmany landfills today producemethane gasand generate power. The aerobic fermentation of biomass produces ethanol,which can find its way as fuel for internal-combustion automobiles.

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It is quite possible that by generating power from biomass locally(e.g., from biowaste), we may enter a new era in power generation wherethe centralized power-generation facilities are part of the past. However,this is speculation, and we anticipate that decentralized power generationfrom biomass and indeed biowaste my start to play an important role in thefuture.

REFERENCES

1. Chum, H.L.; Overend, R.P. Biomass and renewable fuels. Fuel Process Tech-nol. 2001, 71, 187–195.

2. http://www.biomass.org/fact_sheet_2.htm.

3. Biomass Combustion, LIOR International NV, http://www.liorint.com/bio-mass/homebiomass.htm.

4. Nonhebel, S. Energy yields in intensive and extensive biomass production sys-tems. Biomass Bioenerg. 2002, 22, 159–167.

5. Hallam, A.; Anderson, I.C.; Buxton, D.R. Comparative economic analysis ofperennial and annual intercrops for biomass production. Biomass Bioenergy2001, 21, 407–424.

6. van den Broek, R.; Teeuwisse, S.; Healion, K.; Kent, T.; van Wijk, A.; Faaij,A.; Turkenburg, W. Potentials for electricity production from wood in Ireland.Energy 2001, 26, 991–1013.

7. Malik, R.K.; Green, T.H.; Brown, G.F.; Beyl, C.A.; Sistani, K.R.; Mays, D.A.Biomass production of short-rotation bioenergy hardwood plantations affectedby cover crops. Biomass Bioenerg. 2001, 21, 21–33.

8. Zan, C.S.; Fyles, J.W.; Girouard, P.; Samson, R.A. Carbon sequestration in

perennial bioenergy, annual corn and uncultivated systems in southern Quebec.Agric. Ecosyst. Environ. 2001, 86, 135–144.

9. Tuskan, G.A.; Walsh, M.E. Short-rotation woody crop systems, atmospheric

carbon dioxide and carbon management: A US case study. For. Chron. 2001,77, 259–264.

10. Kellogg, R.L.; Lander, C.H.; Moffit, D.C.; Gollehon, N. Manure nutrients

relative to the capacity of cropland and pastureland to assimilate nutrients:Spatial and temporal trends for the United States. US Department of Agricul-ture, National Resource Conservation Center, Economic Research Service,

Publication number NPS-00-0579.11. How America’s diet style is destroying its ground water; Spring: Farm Sanc-

tuary News, 1998.12. Kitani, O.; Hall, C.W. Biomass Handbook; Gordon and Breach Science

Publishers: New York, 1989.13. De Rijk, PJ; Zegwaard, M.J. Literature survey quality organic domestic waste

components (Literatuuronderzoek kwaliteit GFT-componenten), Publicatier-

eeks afvalstoffen VROM, Delft, The Netherlands, 1993/7, 1993.

Biomass Production and Conversion 243

14. Sweeten, J.M.; Korenberg, K.; LePori,W.A.; Annamalai, K. Combustion of cat-tle feedlot manure for energy production. Energy in Agriculture 1986, 5, 55–72.

15. http://www.ecn.nl/phyllis/.

16. http://www.eia.doe.gov/emeu/cabs/usa.html.17. Landbouw Ekonomisch Instituut, Jaarcijfers, 1986.18. http://www.eia.doe.gov/emeu/cabs/euro.html.

19. Graham, R.L.; Allison, L.J.; Becker, D.A. ORECCL—Oak Ridge Energy CropCounty Level Database. Bioenergy 1996: Partnerships to Develop and ApplyBiomass Technologies, Proc. Seventh National Bioenergy Conf., Sept. 5–20,

1996. Nashville, TN. Southeastern Regional Biomass Energy Program, Vol I,552–529; NICH Report No. 24419.

20. http://www.epa.gov/globalwarming/emissions/national/co2.html.

21. Szargut, J.; Morris, D.R.; Steward, F.R. Exergy Analysis of Thermal, Chemicaland Metallurgical Processes; Hemisphere Publishers: New York, 1988.

22. Tillman, D.A. Biomass cofiring: The technology, the experience, the combus-tion consequences. Biomass Bioenerg. 2000, 19, 365–384.

23. Broek,R.;vanden,A.;Faaij,A.;vanWijk.Biomasscombustionpowergenerationtechnologies, Studyperformedwithin the frameworkof the extended JOULE-IIAProgram of CEC DGXII, project ‘‘Energy from biomass: An assessment of two

promising systems for energy production,’’ Department of Science, Technologyand Society, Utrecht University, Utrecht (Report no. 95029), 1995.

24. Hollenbacher, R. Biomass Combustion Technologies in the United States.

Biomass Combustion Conference, Reno, NV, 1992.25. La Nauze, R.D. A review of fluidized bed combustion of biomass. J. Institute of

Energy 1987, 6, 66–76.

26. Advanced Coal-Based Power and Environmental Systems ’98 Conf., session4.2, http://www.netl.doe.gov/publications/proceedings/98/98ps/ps4-2.pdf.

27. Advanced Coal-Based Power and Environmental Systems ’98 Conf., session4.3, http://www.netl.doe.gov/publications/proceedings/98/98ps/ps4-3.pdf.

28. Tillman, D.A. Biomass Bionerg 2000, 19, 265–384.29. Harding, N.S.; Adams, B.R. Biomass Bioenerg. 2000, 19, 429–445.30. State of the art of applied fast pyrolysis of lignocellulosic materials—a review.

Bioresource Technol. 1999, 68, 71–77.31. Bridgwater, A.V.; Meier, D.; Radlein, D. An overview of fast pyrolysis of bio-

mass. Org. Geochem. 1999, 30, 1479–1493.

32. Elliot, D.C.; Beckman, D.; Bridgewater, A.V.; Diebold, J.P.; Gevert, S.B.;Solantausta, Y. Developments in direct thermochemical liquefaction of biomass:1983–1990. Energy and Fuels 1991, 5, 399–410.

33. Meier, D.; Faix, O. State of the art of applied fast pyrolysis of lignocellulosic

materials—a review. Bioresource Technology 1999, 68, 71–77.34. Beckman, D.; Bergh, A.; Elliot, D.C.; Kannel, A. IEA Co-Operative Project D1,

Biomass Liquefaction Test Facility Project, Volume 2: State-of-the–Art Review,

National Technical Information Service, Springfield, VA, DOE/NBM-1062,1988; Vol. 2.

35. Kovac, R.J.; Gorton, C.W.; O’Neil, D.J. Thermochemical Conversion Program

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Annual Meeting; Golden, CO: Solar Energy Research Institute, 1988 (SERI/CP-231-3355), 5–20.

36. Kovac, R.J.; Gorton, C.W.; O’Neil, D.J.; Newman, C.J. Proc. 1987 Biomass

Thermochemical Conversion Contractors’ Review Meeting; National TechnicalInformation Service: Springfield, VA, 1987; (CONF-8705212), 23–40.

37. Roy, C.; de Caumia, B.; Yang, J.; Plante, P. Proc. Seventh Canadian Bioenergy

R and D Seminar; Hogan, E., Ed.; Energy, Mines and Resources Ministry:Ottawa, Canada, 1989; 576–680.

38. Roy, C.; DeCaumia, B.; Pakdel, H. In Research in Thermochemical Biomass

Conversion; Bridgewater, A.V.; Kuester, J.L.; Eds.; New York: Elsevier AppliedScience, 1988; 585–596.

39. Roy, C.; Lemieux, R.; Decaumia, B.; Blanchette, D. ACS Symposium Series No.

376. InPyrolysis Oils from Biomass: Producing, Analyzing and Upgrading; Soltes,E.J.;Milne, T.A.; Eds.; American Chemical Society:Washington, DC, 1988, 16–30.

40. Roy, C.; Pakdel, H. Proc. Seventh Canadian R and D Seminar; Hogan, E., Ed.;

Energy Mines and Resources Ministry: Canada Ottawa, 1989; 681–686.41. Demirbas, A. Energy Conv. Manag. 2001, 42, 1357–1378.42. Klasson,K.T.; Elmore, B.B.; Vega, J.L.; Ackerson,M.D.; Clausen, E.C.; Gaddy,

J.L. Biological production of liquid and gaseous fuels from synthesis gas.Applied Biochemistry and Bioengineering 1990, 24/25, 857–873.

43. http://www.ad-nett.org/html/news.html, DOE/EIA-0603(96) Distribution Cat-

egory UC-950, Renewable Energy Annual 1996, April 1997, Energy Informa-tion Administration, Office of Coal, Nuclear, Electric and Alternate Fuels, U.S.Department of Energy Washington, DC, http://www.eia.doe.gov/cneaf/solar.

renewables/renewable.energy.annual/contents.html.44. Weiland, P. Anaerobic waste digestion in Germany—status and recent devel-

opments. Biodegradation 2000, 11, 415–421.45. Energy from Waste, Irish Energy Centre, 2002, Archive 94, http://www.irish-

energy.ie/publications/index.html.46. http://www.tva.gov/greenpowerswitch/landfill_faq.htm.47. Liu, H.W.; Walter, H.K.; Vogt, G.M.; Vogt, H.S.; Holbein, B.E. Steam pres-

sure disruption of municipal solid waste enhances anaerobic digestion kineticsand biogas yield. Biotechnology and Bioengineering 2002, 77, 121–130.

48. Purohit, P.; Kumar, A.; Rana, S.; Kandpal, T.C. Using renewable energy tech-

nologies for domestic cooking in India: A methodology for potential estimation.Renewable Energy 2002, 26, 235–246.

49. Misi, S.N.; Forster, C.F. Batch co-digestion of two-component mixtures ofagrowastes. Process Safety andEnvironmental Protection2001,79 (B6), 365–371.

50. http://www.nrel.gov/international/applications.html.51. http://www.eren.doe.gov/consumerinfo/refbriefs/ab5.html.52. Ethanol: Separating Fact from Fiction, 4/99, http://www.ott.doe.gov/biofuels/

publications.html#bioethanol.53. U.S.EnvironmentalProtectionAgency,OxygenatedFuelsProgram,citedin[55].54. Fuel-Cycle Fossil Energy Use and Greenhouse Gas Emissions of Fuel Ethanol

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Produced from U.S. Midwest Corn, Center for Transportation Research, Ar-gonne National Laboratory, Dec. 1997.

55. Fuel Cycle Evaluation of Biomass-Ethanol and Reformulated Gasoline, Bio-

fuels Systems Division, U.S. Department of Energy, July 1994.56. Technology Brief—NREL Getting Extra ‘‘Corn Squeezins’’ (Cooperative

Agreement Uses Cellulosic Fiber to Get More Ethanol from Corn), N.V. 1993.

57. Biodiesel Handling and Use Guidelines, http://www.ott.doe.gov/biofuels/publications.html bioethanol.

58. Goudriaan, F.; Peferoen, D.G.R. Liquid fuels from biomass via a hydrothermal

process. Chem. Eng. Sc. 1990, 45, 2729–2734.59. Goudriaan, F.; van de Beld, B.; Boerefijn, F.R.; Bos, G.M.; Naber, J.E.; van

der Wal, S.; Zeevalkink, J.A. Progress in Thermochemical Biomass Conversion,

Tyrol, Austria, Sept. 18–21, 2000; Bridgewater, A.V., Ed.; 2000; 1312–1325.60. Zhong, C.; Peters, C.J.; de Swaan Arons, J. Thermodynamic modeling of

biomass conversion processes. Fluid Phase Equilibria 2002, 194–197, 805–815.61. Feng, W.; van der Kooi, H.; de Swaan Arons, J. Chemical Eng. and Proc.

in press.

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17Green Chemistry

In this chapter* we touch on the concept of green chemistry. We discuss thelink between green chemistry and sustainability and give some examples.

1 INTRODUCTION

In the 1950s and 1960s chemistry was seen as the solution to a host of society’sneeds and problems. By grace of the discoveries in the field of chemistry, wehave many goods today, which we take for granted. The way to differentpolymers was paved by the discovery of Ziegler–Natta catalysis. Develop-ments in the field of solid-state chemistry open vistas for integrated circuittechnology and the current information technology boom. These days, largeparts of computers and automobiles are synthetic and are of polymer origin.Simultaneously, chemical conversion of crude oil to gasoline, and other pro-ducts, has helped economies around the world enjoy a level of unprecedentedprosperity.

Unfortunately, amid many success stories due to chemistry, there weresome adverse outcomes that had not been foreseen. The highly successfulinsecticide dichlorodiphenyltrichloroethane [DDT, or 1,1-bis(4-chloro-phenyl)-2,2,2-trichloroethane] would cause bioaccumulation in birds andother animals. This caused eggshell thinning and nesting failures, which inturn led to drastic population declines in various bird species. Tetraethylleadwas used as an antiknock agent in gasoline until it was learned that it wascausing lead poisoning and lowering the IQ of children.

Today, there is a suspicion of scientists, and ‘‘chemophobia’’ has in-creased [1]. People view chemistry as the source of the planet’s pollution. It

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*Adapted from [1].

seems that the time is right for green chemistry. What is green chemistry?The American Chemical Society defines it as follows:

Green chemistry is the design of chemical products and processes thatreduces or eliminates the use and generation of hazardous substances.Green chemistry is environmentally benign, linking the design of chem-

ical products and processes with their impacts on human health and theenvironment. [2]

In this way, adverse outcomes will be minimized. There is a myth that greenchemistry will cost more. This might be true if something was to be added atthe smokestack or outlet pipe. However, if the whole process is examinedand rethought, being green can save money. For example, a process may usean organic solvent of which a certain proportion leaks into the air, thuscontributing to air pollution. If the solvent is captured and recycled to theprocess, the savings from not having to buy fresh solvent may be greaterthan the cost of the equipment that recycles it. If the process is converted toa water solvent-based one, there may be additional savings, since water ischeaper than organic solvents. To understand how green chemistry works,we will examine some cases dealing with alternatives to ‘‘conventional’’chemistry and green chemistry itself. In Section 2, we examine toxic metalions, and in Section 3, we discuss organic solvents. Section 4 deals with ma-terials for a sustainable economy, while Section 5 discusses recycling. Weconclude with Section 6.

2 TOXIC HEAVY METAL IONS

The toxicities of heavy metals are well known. These include cadmium,chromium, cobalt, copper, lead, mercury, tin, and zinc. Materials containingthesemetals have been used quite extensively; for example, cadmium in nickel-cadmium, silver-cadmium, and mercury-cadmium batteries; chromium in thetanning of leathers and the dyeing of textiles; cobalt for catalysis in the oxoprocess and in p-xylene oxidation; lead compounds as antiknock agents ingasoline; and mercury in biocides in latex paints. The effects of toxic heavymetals on humans, plant, and animal life are well documented. Various ap-proaches are being studied in an effort to eliminate or minimize the problemsassociated with toxic heavy metals while not doing away with the end uses.

Some heavy metals are released into the environment as a byproduct.It would be preferable to eliminate the sources of these toxic heavy metals;for example, precipitation of mercury as the sulfide leaves mercury in theeffluent streams of certain chloro-alkali plants. There can be considerablebio-accumulation of mercury, resulting in river fish not being suitable for

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consumption. If these plants switch to a Nafion (a perfluorinated polymericsulfonic membrane) membrane process, no mercury is required, and the mer-cury stream is eliminated. Another example is that of antifoulant coatings forships. They work by slowly leaching a toxicant in the water. Copper oxide isused, as well as tributyltin compounds . When the ships are in the deep ocean,there is no problem with the tin compound as the dilution is larger. However,when the ship is in port (which is the case for recreational boats), the metalcompound can kill desirable animals in the harbor. Elevated levels oftributyltin compounds have been found in stranded bottlenose dolphins [3]and is an example of an unwanted biocide. Rohm and Haas have provided acompound (isothiazolone) that can last for three years, is more environmen-tally friendly [4], and does not lead to undesirable side effects. Anothercompound as a monomer is said to lead to polymers with an antifoulantactivity [5], which could have possible future applications. Many sessileanimals in the sea are not fouled by the algae, hydroids, mussels, and so onthat foul ships, cooling systems of powerplants, and aquaculture cages.Numerous investigators are studying the chemical defenses of aquatic life inan effort to identify the biological antifoulants. Many compounds have beenisolated, and it is hoped that total synthesis methods can be used to producethese.

The search is on for catalysts to replace those containing heavy metals.For example, the addition of hydrogen chloride to acetylene to form vinylchloride is catalyzed by mercuric chloride. Rhodium (III) chloride on ac-tivated carbon works just as well and is much less toxic [6]. Spent catalystsneed to be reclaimed either on site or at a central-processing facility, ratherthan being sent to a landfill. However, withmetals that are not toxic, it is oftencheaper to recycle them to other uses. The reduction of 2-2-ethyl-2-hexenal to2-ethylhexanol can be catalyzed by a mixture of copper, zinc, manganese, andaluminum oxides in 100% yield [7] and is an alternative to the carcinogeniccopper chromite. Spent nickel catalysts often end up in stainless steel, and inthis way thousands of tons of catalyst can be recycled.

In short, the problem of toxic heavy metals can be tackled by seekingalternatives that are not a burden to the environment, the health of man,or the safety of the plant worker and that can be cost-effective as well (i.e.,by higher specificity in catalysis).

3 SOLVENTS

The use of solvents is not new to chemistry. In fact, solvents are very useful.They can be used to (1) place reagents in a common phase where theyreact (the amount of solvent is in part determined by the solubility limits of

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the reactants), (2) act as good heat transfer agents to control the temper-ature in exothermic reactions, and (3) clean equipment and clothing, amongother things. An estimated 160 billion gallons of solvent is used annually inthe United States alone [8]. Vapor degreasing is the largest use, followed bydry cleaning and immersion cleaning of parts. Some disadvantages ofsolvents include (1) destruction of the upper atmosphere by chlorofluorocar-bons, (2) toxicity to workers of some chlorinated solvents, and (3) monetarycost due to loss of some 10–15million tons of solvents ($2 billion) each year. Asimple tiered approach may be suggested to tackle the issue of solvents:

1. Place something on the plant outlet to destroy or recover the sol-vent.

2. Enclose the operation so that the solvent is not lost.3. Substitute with a less harmful solvent.4. Use supercritical carbon dioxide as a solvent.5. Use water.6. Use no solvent.7. Switch to another process that requires no solvent.8. Can we do just as well without the product made with the solvent?

Reichhold Chemical in Dover, Delaware, uses a gas-fired incineratorto destroy emissions of solvents, which is one of the ways of destroying orrecovering solvent [9]. Some dry cleaners have reduced their use of perchlo-roethylene by 96% by using new, tighter equipment and a system that filtersand redistills used solvent. The payback period for the initial investment wasfour years [10].

Recovery of used solvents by distillation is much easier if each solventis stored separately. A single solvent for the whole plant would be desirableif a solvent has to be used. Novartis has done this for a process, with theresult that it now produces only 1.5 lb waste per pound product instead ofthe former 17.5 pounds [4]! The initial investment was $2.1 million, and theannual savings are $775,000.

Many industrial reactions are carried out in the gas phase usingheterogeneous catalysts, thus eliminating the use of solvents. For example,methanol is made from synthesis gas (CO and H2) using zinc oxide-con-taining catalysts. The heat is controlled by injecting cold feed at variousplaces in the reactor. Oxidation of methanol to formaldehyde with oxygen isdone in the gas phase, with an excess of methanol to keep the mixtureoutside the explosion limits.

At times excess starting material can actually serve the role of thesolvent. Excess liquid chlorine has been used in the chlorination of naturalrubber to eliminate the usual carbon tetrachloride, since it is very difficultto remove the last traces of carbon tetrachloride from the rubber [11]. The

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current literature contains many reactions that are run without a solvent.Frequently, this can offer improved yields and selectivity as well as simplicity.Almost all of them still use some solvent in the workup and sometimes in-volve chromatographic separations. This solvent might be avoided byfiltering off a solid catalyst, then using it in the next run without washing itwith solvent to recover the last product. The goal is to find simple, con-venient, fast, energy-efficient ways to isolate the product and to recycle anycatalysts and support. For example, aldehydes can be condensed with ali-phatic nitro compounds using an ion-exchange resin [12] or a potassiumexchanged-layered zirconium phosphate as a catalyst [13]. The yields were62–83%. The ion-exchange resin and the zirconium phosphate were washedwith hazardous methylene chloride to recover the products. The catalystcould be reused with little loss in activity.

4 MATERIALS FOR A SUSTAINABLE ECONOMY

Most organic chemicals in use today are derived from nonrenewable pe-troleum and natural gas, with a small proportion still made from coal. Afteruse, the products ultimately end up as carbon dioxide, the main greenhousegas causing global warming. For a sustainable future, increasing carbondioxide levels is not desirable, and the closing of elemental cycles should bepursued. In other words, renewables from fields and forests should be uti-lized where possible.* Before the advent of the petroleum era, many pro-ducts were made using renewables, and it would be instructive to examinethe viability of these old techniques.

The largest volume chemical produced in 1995 in the United States [14]is ethylene (46.97 billion lb), followed by ammonia (35.60 billion lb) andpropylene (25.69 billion lb). These compounds are frequently used to formpolymers such as polyethylene (41% of the world’s total) and polypropylene(21% of the world’s total) [15].

Before the advent of petroleum,many natural polymers were being usedor being studied for use in plastics. Since then, however, synthetic polymershave dominated the marketplace. It should be possible to make plastics thatwe need from cellulose, starch, lignin, or other natural products.

Cellulose is found in wood, along with hemicellulose and lignin, and incotton, linen, hemp, and other similar products. It is a polymer of glucose. Itcan also be made from sucrose by bacterial means [16]. This bacterial cel-

*For example, methane derived from anaerobic fermentation is a renewable source, but there is

not enough biomass to supply the methane to satisfy the worldwide fuel demand.

Green Chemistry 251

lulose has high mechanical strength and may become an important materialif the cost can be brought down.

Regenerated cellulose fibers are known as rayon and regenerated filmsas cellophane. They are made by the xanthate process, which uses sodiumhydroxide and carbon disulfide:

CellOH!NaOHCellO�Naþ!CS2 CellOCðSÞS�Naþ!H

þCellOH ð1Þ

The xanthate solution is converted to fiber or film by passage into a bathof acid. This relatively polluting process can be, and is being, replaced by aprocess in which a solution of cellulose in N-methylmorpholin-N-oxide ispassed into water [17–21]. The solvent is recovered and recycled. This methodproduces stronger materials, because the resulting molecular weight is higher.

A possible way to lower the costs of fibers and films of regeneratedcellulose would be to run cellulose through a twin-screw ultrasonic extruderwith a minimum of solvent and pass the extrudate through a stream of hotair to recover the solvent for reuse. This stronger cellophane could be usedin place of many plastic films used today. A great number of derivates ofcellulose have been made. Methyl, ethyl, carboxymethyl, hydroxyethyl, andhydroxypropyl ethers are made commercially today. These are used as water-soluble polymers, except for ethylcellulose, which is a tough plastic used inscrewdriver handles and such.

The hemicellulose from the pulping of trees is an underused resource.A small amount is currently being hydrolyzed to xylose for hydrogena-tion to the sweetener xylitol. A good use could be as a substrate for fermen-tation.

Many examples of materials for a sustainable economy can be foundby lateral thinking and good chemistry. A comprehensive list is given in [1].

5 RECYCLING

The minimization of waste is an important issue. Recycling is a good optionbut should only be considered if reuse is not possible. For a sustainablefuture, it is necessary to recycle as much as possible. The amount of wastevaries from country to country, with the United States leading the list with0.88 ton per person per year, followed by Australia (0.74 ton per person peryear) and Canada (0.5 ton per person per year) [22,23]. Only 27% of themunicipal solid waste generated in the United States in 1995 was recycled.Materials typically recycled included paper, plastic, wood, steel, aluminum,and glass.

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Recycling is simplified if the material is free of contaminants. Thisrequires as much separation as possible at the source. However, this processis complicated because many consumer items consist of more than one ma-terial. Furthermore, materials such as paper, steel, aluminum, glass, andplastic come in different grades and compositions. For example, some papermay be dyed or waxed. Window glass has a different composition than thatcommonly found in containers and must be kept separate.

Some curbside recycling programs allow the comingling of materialsthat are easily separated to save work for the consumer. For example, steelcan easily be separated from aluminum by use of a magnet.

The re-use or recycling of paper has advantages on incineration torecover energy from it [23–27], despite contrary claims by some authors.Recycling saves more energy than that obtained by incineration, becausemaking new paper requires energy to harvest new trees, and so on. Recyclingcreates three times as many jobs as incineration. In England, recycling helpsthe balance of payments and avoids landfill costs. People who recycle paperare working toward a goal of 100% recycled fiber content, with zerowastewater discharge from the plant. In a few instances, this is possible today[1]. As the techniques of recycling gradually improve, the postconsumercontent of recycled paper is rising.

Some paper can be recycled without de-inking. The resulting sheet willbe somewhat gray but can be reprinted in a legible fashion. For some uses,such as toilet tissue, there should be no need for de-inking or bleaching.However, in most cases, de-inking is required, and the degree of de-inkingdepends on the ultimate use.

The removal of toners and inks used in photocopiers can offer problems.Toners are low-melting resins containing carbon black. Various techniquesare employed to facilitate their removal. One way is to melt them during thede-inking process, so they can conglomerate, then cool the mixture to hardenthem, and remove them by screens. Ultrasound can be used to break up thetoner particles for easier removal as well.

Mixed waste paper can also be utilized for uses other than paper. Theuses include (1) molding of paper fibers mixed with polyethylene or poly-propylene to form door panels, trunk liners, and plastic lumber, (2) non-woven mats of up to 90% paper fibers held together by synthetic fibers, and(3) composites of wood, paper fiber, and gypsum.

In short, a lot can be done using recycling. Also the reduction of theamount of waste is also a good step toward a sustainable society. Forexample, use of a drinking glass eliminates the use of a disposable polysty-rene cup. Bringing shopping bags (as is common in The Netherlands) elim-inates the use of disposable plastic bags. Also, if less material can be used to

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make more of the product (by improving, e.g., mechanical strength of theplastic so the bottle can be thinner), less waste will be generated.

6 CONCLUDING REMARKS

We hope to have shown in this chapter that the use of green chemistry cancontribute to a sustainable society. However, the benefits are also monetary:Recycling and reuse of solvents can be cost-effective as is the recycling ofpaper. Changing to renewable materials is beneficial since they comprise anessential infinite source. At the heart of green chemistry lie innovation andthe ability to ask the question ‘‘why?’’ But to answer this question we mustknow what sustainability in a technological context and we will go into moredetail in Chapter 18.

Why should a certain process use a certain process route which canhave a negative impact on the workers or environment? Is an alternative notavailable? Why should a certain material be used in an application? Cananother one be used that lasts longer and is cheaper? To answer these ques-tions, one has to be innovative, and these answers lead to green chemistry.We wish to point out that this chapter only touches on green chemistry, andthe interested reader is referred to [1] for a comprehensive treatment of theprinciples.

Finally, we wish to point out that even though technology may beavailable to produce a product from a renewable source, this does not nec-essarily imply that the technology is truly green. For example, it is tech-nologically possible to make plastics from plants rather than fossil fuels [28].A study [28] showed that the fossil energy demands imposed by the sep-aration and purification of the solvent and plastic would be much larger thanthose of petrochemical routes! Therefore, caution should always be takenwhen evaluating green technologies to ensure they are truly green as a whole.With time, technologies can change and become more energy-efficient, thuschanging the picture, since the petrochemical industry has benefitted fromyears of research in increasing efficiency. What this example teaches us is thatwe must remain ever vigilant and openminded, and perhaps pursue technol-ogies that shift paradigms and have much larger potential benefits to societyand the environment.

REFERENCES

1. Matlack, A.S. Green Chemistry; New York: Marcel Dekker, Inc., 2001.2. http://www.acs.org/education/greenchem/.

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3. Kannan, K.; Senthilkuman, K.; Loganathan, B.G.; Takahashi, S.; Odell, D.K.;Tanabe, S. Environ. Sci. Technol. 1997, 31, 296.

4. Presidential Green Chemistry Challenge. EPA 744-K-96-001, July 1996, 4.

5. Kim, B.S.; Seo, C.K.; You, C.J. U.S. Patent 5,472,993, 1995.6. Panova, S.S.; Shestakov, G.K.; Temkin, O.N. J. Chem. Soc. Chem. Commun.

1994, 977.

7. Furstner, A.; Shi, N. J. Am. Chem. Soc. 1996, 118, 2533.8. Gavaskar, A.R.; Offenbuttel, R.F.; Hernon-Kenny, L.A.; Jones, J.A.; Salem,

M.A.; Becker, J.R.; Tabor, J.E. Onsite Solvent Recovery. U. S. EPA/600/R-94/

026, Cincinatti, OH, Sept. 1993.9. Mills, B. Surf. Coat. Int. 1998, 81, 223.10. Farrell, A. Delaware Estuary News 1996, 6, 6.

11. Cataldo, F. J. Appl. Polym. Sci. 1995, 58, 2063.12. Ballini, R.; Bosica, G.; Forconi, P. Tetrahedron 1996, 52, 1677.13. Constantino, U.; Curini, M.; Marmottini, F.; Rosati, D.; Pisani, E. Chem. Lett.

1994, 2215.

14. Kirschner, E.M. Chem. Eng. News Apr. 1996, 17, 8.15. Reich, M.S. Chem. Eng. News May 1997, 14, 26.16. Tajima, K.; Fujiwara, M.; Takai, M. Macromol. Symp. 1995, 99, 149.

17. Mortimer, S.A.; Peguy, A.A. J. Appl. Polym. Sci. 1996, 60, 305, 1747.18. O’Driscoll, C. Chem. Br. 1996, 32 (12), 27.19. Dobson, S. Chem. Ind. (London) 1995, 870.

20. Parkinson, G. Chem. Eng. 1995, 103, 10.21. Hirami, M. J. Macromol. Sci. Pure Appl. Chem. 1996, A33, 1825.22. Levy, G.M., Ed.; Packaging in the Environment; London: Blackie Academic

and Professional, 1993.23. Matos, G.; Wagner, L. Ann. Rev. Energy Environ. 1998, 23, 107.24. Berman, F. Trash to Cash; Delray Beach, FL: St. Lucie Press, 1996.25. Thompson, C.G. Recycled Papers—The Essential Guide; Cambridge, MA: MIT

Press, 1992.26. Bateman, B. Pap. Technol. 1996, 37, 15.27. Karna, A.; Engstrom, J.; Kutinlahti, T. Pulp Pap. Can. 1994, 95, 38.

28. Gerngross, T.U.; Slater, S.C. How green are green plastics? Scientific American,Aug. 2000.

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18Economics, Ecology,and Thermodynamics

In this chapter we pay attention to the emerging role of ecology in economicmodels and theories. Next we discuss what has been launched as eco-

thermodynamics or the role of the fundamental laws of thermodynamics ineconomics and the prominence of the exergy concept. We then show how theprinciples of a thermodynamic analysis can be transplanted from a purelyengineering application to an economic analysis. The relation between ecol-ogy and thermodynamics is illustrated with two selected examples of greenchemistry. Finally, we make a plea for integrating disciplines such aseconomy, ecology, and science and technology, whenever important andwell-founded recommendations have to be made to governing authorities.

1 INTRODUCTION

Economics is the science of economy, economy being ‘‘the management of ahousehold or state, its income and expenditures,’’ andmore particularly, ‘‘thecareful management of its wealth and resources’’ [1]. Ecology is concernedwith the relations between living organism and their environment. Animportant aspect of these relations is the exchange and conversion of energyand matter. And so it is not too surprising that many consider thermody-namics, being the ultimate science of the transformation of energy andmatterand always dealingwith the exchange between systems and their environment,as essential for inclusion into any economic and ecological analysis.

In appearance thermodynamics seems to be nothing more or less than anice collection of abstract mathematical relations between the properties ofmatter valid for the various states in which this matter may prevail. It be-comes more substantial when thermodynamics is applied, as in process tech-nology. The extent to which one form of energy (e.g., heat) can be converted

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into another (e.g., work) or to which one form ofmatter (e.g., methane) can beconverted into another form of matter (e.g., methanol or hydrogen) istraditionally governed by thermodynamics. But even if such conversionsappear to be ‘‘technologically’’ feasible, their practical realization may stilldepend on the economic viability. Monetary units such as the dollar andconcepts such as the cost of production factors such as labor and capital enterthe analysis and often dominate the outcome. Interestingly enough, labor andcapital relate more and more often to the environment: What is the cost torepair the burden of technology on the environment? More sophisticated, thefollowing question is raised:What part of the cost relates to the cost of naturalcapital such as forest, the ocean, or the soil and of natural services such aswaste assimilation? So the relation between and interwovenness of economyand ecology are clear, but the relation of these disciplines with thermody-namics is less obvious. However, in Chapter 13, when analyzing economicsystems and their interaction with the environment, it becomes clear thateconomic systems, whatever their details, appear to be driven in the samedirection as the industrial or agricultural processes that constitute them, thatis, the direction prescribed by the second law, namely the direction of entropyproduction, the formation of waste, or the dissipation of useful work. In thesubsequent sections we endeavor to illustrate how close the relationship oftenis among thermodynamics, economics, and ecology.

The case of sustainable development or, as some prefer, the develop-ment toward sustainability is illustrative for the general observation that thereis a conflict between short-term and long-term values. To quote the famoussociobiologist E. O. Wilson,

To select values for the near future of one’s area of responsibility is rela-tively easy; to select values for the distant future of the whole planet isrelatively easy too—in theory at least. To combine the two visions to

create a universal environmental ethic is very difficult. But combine them,

we must. [2]

2 ECONOMICS* AND ECOLOGY

The authors of this book are all engineers and do not claim much more thanthe layman’s understanding of both economics and ecology. In addition, theyrely on some distinct authors and their publications [2–7] and, not in the least,on their own common sense, which has developed in many years of engineer-ing practice, both in industry as well as in academia. Their understanding isthat economics is about the production of goods and services (Fig. 1a),production realized by so-called production factors such as capital and labor,and about monetary flows while, much to their surprise, that the flows of

Chapter 18258

energy and matter are much less important. Economic activities are capturedin more or less precise models. Conventional economists have a strong beliefin price and market mechanisms. All economic activities are expressed inmonetary flows. Economic performance and growth are measured, in mon-etary terms, at current prices in the so-called gross national or domesticproduct (GNP or GDP), which acts as a macroeconomic indicator and isconsidered to be a universal yardstick. Conventional economists seem to havegreat optimism about resource supply and absorptive capacity of the envi-ronment and an infinite faith in human ingenuity to solve problems wheneverthey occur and whatever their nature, for example, environmental problemsor questions about the so-called carrying capacity of this planet.

As mentioned in Chapter 13, environmental or ecological economistsdisagree largely with this picture and attitude and insist on some majoradjustments of prevailing economic ideas. For one thing, ecological econo-mists consider economic activity constrained by the regenerative capacity ofthe ecosphere, namely that part of the planet containing living organisms. Theeconomy is contained by the ecosphere [7] and as such is dependent on theservices supplied by this ecosphere (Fig. 1b). However, market prices maskthe role and contribution of these services and the natural capital that suppliesthese services. Services rendered by natural capital are not accounted for andthus, in our monetary world, not valued. The price of a depleting resource,like oil, may go down to less than US$10, as happened a few years ago, whichdoes not account for oil’s longer-term scarcity, but at most for its currenttemporary abundance. Equally, market and price mechanisms do not re-flect ecofunctional scarcity, rather short-term demand. In the sharp words ofGeorgescu-Roegen [9]:

The savage deforestation which at one time menaced all the woods inthe world was the result of the fact that the prices were right. And it wasnot brought to a halt by the price mechanisms, but only by the intro-

duction of some quantitative restrictive rules.

And if the cheetah is now an endangered species, it is because the priceof a cheetah pelt is just right for some people to hunt one animal after

the other.

* The first author (JdSA) wishes to acknowledge the contributions of Robert U. Ayres and

Stefan Baumgartner. Their work gave him much inspiration and insight after meeting them at

a Gordon Research Conference meant to cross the frontiers of thermodynamics. Both

scientists are physicists by training but turned to economics in the course of their careers. In

our opinion they are invaluable in all serious efforts to incorporate science’s fundamental laws

into economic theories. This will be in everybody’s interest, as economists appear to be

extremely influential in important and far-reaching government decisions [8].

Economics, Ecology, and Thermodynamics 259

Figure 1 The economic system of producing and consuming goods and services.(a) Excluding the interaction with its environment. (b) Including the interaction with

its environment. The direction of the overall process is unidirectional, namely fromleft to right.

Chapter 18260

Another important objection to conventional economic wisdom ismonetary appraisal as in project appraisal or evaluation. There is a prejudiceto the future by discounting; the present value of future benefits may beexceeded by the immediate short-term benefits [7]. Application of what somehave called a revolution in investment analysis (i.e., investment underuncertainty [10]) may alter this, for example by accounting for possibleincreased scarcity of ecological services [5]. Discounting makes nature appearless valuable the farther we look into the future, although future generationsmay need at least the same amount of ecological goods and services we needtoday, whatever the discount rate may be. Should we not account for thiswhenever natural capital (a piece of land) is transformed into human-madecapital (a shopping center) [7]?

So expressing economic activities in terms of monetary flows has anumber of serious disadvantages, the main ones being that goods and servicesfrom natural capital are ignored and that it is, for the moment, impossible toexpress these contributions in terms of money. But let us first look at thecomponents of these resources and estimate their financial size.

In 1997Costanza and his co-workers published a revelating article in thejournal Nature entitled ‘‘The value of the world’s ecosystem services andnatural capital’’ [5]. Their starting point was the concern that ecosystemservices are not fully ‘‘captured’’ in commercial markets or well comparedwith manufactured capital and economic services and thus given little weightin policy decisions. They studied 16 marine and terrestrial biotic communitiessuch as oceans, deserts, and forests and tried to estimate the current economicvalue of 17 renewable ecosystem services. Services comprise goods, such asfood, and services, such as waste assimilation. These services, which consist offlows of materials, energy, and information, as contained in natural capitalstocks, and albeit not visible in GNP or balance sheets, are combined withmanmade goods and services to produce human welfare. Major categories ofecosystem services consideredwere food production, nutrient recycling, wastetreatment, and recreation, among others. Estimating the global gross nationalproduct to be around US$18 trillion (=18 � 1012), the authors estimate theminimum current economic value of these ecosystem services to be in therange of US$16–54 trillion per year. The authors conclude that if one were totry to replace these services—supposing this is possible, which of course it isnot—the global GNP would nearly triple without any increase in welfare. Ifecosystem services were paid for, the global price system would be verydifferent, in particular for products using these services. Another conclusion isthat although economic welfare has significantly increased in terms ofconventional GNP, correcting for ecosystem services shows that not muchimprovement has taken place since 1970. Finally, the authors point out thatthe impact that such estimates will make, if they are included in project

Economics, Ecology, and Thermodynamics 261

appraisals, is considerable. It would take away the earlier objection againstdiscounting procedures in economic analysis, as these are biased against thefuture. In this new analysis, natural capital and ecosystem services are likely tobecome more scarce in the future and thus more valuable rather than lessvaluable.

There have been some prudent other efforts to make a start withcorrecting the GNP for factors such as the deterioration of the quality of lifeand the natural environment. In the Green GNP, deductions have beenintroduced for goods and services required for environmental protection [6].Such corrections can easily lead to a 10% reduction in the GNP or a 50%reduction in economic growth. In Japan, the Economic Planning Agency(EPA) formulated a new economic indicator called National Net Welfare(NNW). The EPA’s estimates were that the NNW is 12% less than Japan’sGNP [6].

Nevertheless, the Japanese question how to quantify environmentaldamage and how to translate this into monetary value. It is obvious that aglobal approach is required; a country taking measures on its own may beeasily ‘‘out-competed’’ by countries that do not take measures at all. Otheraspects are that pollution (e.g., in the form of waste) can be ‘‘exported’’ andproductive land ‘‘imported’’ (e.g., citrus fruit imports), which does not add tothe solidarity that the world’s citizens must eventually develop.

Wewould like to conclude this sectionwith a reference to a book excerptthat has appeared in the February 2002 issue of Scientific American. Thebook, The Future of Life, is written by Edward O. Wilson, whom we cited atthe end of the last section [2]. Wilson claims that environmentalism is muchmore than a special-interest hobby. Its essence has been defined by science.The earth is not in physical equilibrium (see the next section on eco-thermodynamics); its nonequilibrium condition needs to be sustained withthe help of an extraneous energy source that is driving numerous cycles ofmatter and energy, emulating each other in complexity. The fragility of theseself-organized cycles is for many of greater concern than the finite capacity ofthe environment to supply resources or absorb waste [11]. A major under-standing of this biosphere is required for many purposes. One such purpose isthe proper analysis of economic activities. Apart from establishing theultimate carrying capacity of this planet (10 or 16 billion people?), it isnecessary to include the cost of ecosystem services in any economic analysis.After all, such an analysis is aimed not only at helping us to sustain our ownprosperity in the near future but also at helping our offspring to achieveprosperity in the distant future, one of the main goals defined in the Brundt-land report [12].

One cannot help but reflect Man’s position in Nature. Up to a certainperiod in the past, Man fitted nicely in nature’s cycles and did not disturb its

Chapter 18262

course. ThenMan stepped out of the prevailing cycles and, while entering theIndustrial Revolution, may have started to disturb this course. Is it naive toconclude for the moment that the only way to repair this situation is tobecome part again of Nature’s cycles?

3 ECO-THERMODYNAMICS

This section is based mainly on the article ‘‘Eco-thermodynamics: Economicsand the Second Law,’’ by Robert U. Ayres, in which he discusses economicsand the main laws of thermodynamics, in particular the second law [11]. Bothlaws have significant implications for economic theory but do not seem toreach economists albeit that engineers cannot properly designmany industrialprocesses without these laws! Engineers, like ourselves, oftenmiss the point ofeconomists when the latter claim that capital and labor are the essentialproduction factors, not resources (i.e., exergy). This view suggests that thecook (labor) and the kitchen (capital) do not require flour, sugar, or eggs tomake a cake.

The first law is concerned with the conservation of mass and energy,with the exception of nuclear transformations, which would be required toinclude Einstein’s postulate of the equivalence of mass and energy. Figure 2

Figure 2 The first law at steady state, En1 + En2 = En3 + En4. Arrows may alsopoint in the opposite direction.

Economics, Ecology, and Thermodynamics 263

depicts a process with energy flows entering and leaving the process. The firstlaw requires that

En1 þ En2 ¼ En3 þ En4 ð1Þand does not comment on the direction of the process: All arrows could as wellpoint the other direction. The second law is concerned with the direction ofthe process and postulates that this direction is the one in which entropy isgenerated when considering the system and its environment together. InChapter 5 we show the relation between entropy generation and work lost:

Wlost ¼ T0Sgen ð2ÞSo another interpretation of the second law is that the direction of the processis the direction in which available work dissipates. In Chapter 6 we introducethe concept of the quality of energy, defined as

qiuExiEni

ð3Þ

expressing the part of energy from Eni that is available for work, while usingour environment as a reference. The direction of the process depicted in Fig. 2is thus correct, provided

En1 � q1 þ En2 � q2 > En3 � q3 þ En4 � q4 ð4Þexpressing that the direction of the process is that direction in which thequality of all energy involved degrades (Fig. 3). Equation (4) combined withEq. (2) can be written as

Exlost ¼ T0Sgen ð5ÞThis is whyAyres prefers the exergy concept over the entropy concept becausethe latter contains, in his words, toomuch ‘‘mystical baggage.’’Wewould liketo add that in order to reach economists, and we should make every effort todo that, the term ‘‘available work’’ should be preferred over ‘‘exergy,’’ as inour opinion the latter concept still contains too much ‘‘mystical baggage.’’

The laws of mass and energy conservation and the second law combinedgive a sharp insight into the industrial process, its resources, waste, and losses(Fig. 4). We wish to illustrate this in a simplified example [13]. Suppose wewant to produce metal X from its oxide XO, which is readily found in natureas a resource. The most elementary reaction to handle this transformation is

XO ! X þ 1

2O2 ð6Þ

Chapter 18264

In a handbook such as Szargut et al. [14], these values are tabulated and theexergy values of XO and X are found, for example, to be 50 and 500 kJ/mole,respectively. So this reaction requires an amount of exergy of at least some 450kJ/mole product. Usually this is supplied by a nonrenewable fuel such as coal,oil, or gas (the exergy of oxygen is small and has been neglected). Fromliterature we learn that a suitable reactant, at the same time a supplier of

Figure 4 Thermodynamic analysis of waste generation. (From Ref. 15.)

Figure 3 The second law at steady state. If En1q1 + En2q2 > En3q3 + En4q4, thenthe arrows point right. (From Ref. 3, 15.)

Economics, Ecology, and Thermodynamics 265

exergy, is carbon (with an exergy value of 410 kJ/mole, but for simplicity weassume 400 and as resource ‘‘coal’’)

XOþ 1

2C! Xþ 1

2CO2 ð7Þ

This equation expresses the law of the conservation of mass, overall and foreach chemical element separately. However, a quick calculation shows thatfor this reaction to be possible thermodynamically we are still short of exergy:50 + 1⁄2 � 400 equals 250 kJ/mole product, short of the 500 + 1⁄2 � 20 at theproduct side. So at least another half mole of carbon is required to make thereaction thermodynamically possible. Meanwhile, we are building up sub-stantial amounts of waste in the form of CO2. And if we account for, let us say,the 50% thermodynamic efficiency with which this process supposedly isknown to be carried out according to the newest technology, then this amountof waste may double. We observe that we have drawn from nonrenewableresources and emitted waste at nearly five times the rate corresponding to thatfor the reaction [Eq. (7)]. Of course, this is all a consequence of choosing amaterial, nonrenewable resource, coal, as the reactant and supplier ofrequired chemical work: The use of fossil fuel and the inefficiency of processesare responsible for most of the waste in industry. Figures 5 and 6 give animpression of the size of waste [15], where we should note that in the chemicalindustry things quickly get worse if we move, for example, from basechemicals to fine chemicals to pharmaceuticals.

Relief may be offered if we move from nonrenewable fuels to arenewable exergy source such as sunlight. But this would require completelynew technology at acceptable efficiencies. One might envisage, for example,the photolytic dissociation ofwater to produce hydrogen, hydrogen taking therole of carbon in reducing XO toward the pure metal X. But the efficiency ofphotolysis so far is a few percent [16], so considerable amounts of exergy will

Figure 5 The size of waste for Germany in 1990. (From Ref. 15.)

Chapter 18266

be required to manufacture all equipment required for operation. Most likelythis exergy has to be ‘‘advanced’’ by fossil resources, which have temptedsome to point out that solar energy applications and, perhaps, a more generalother renewable energy will be based mainly on fossil fuel consumption (see,e.g., [9]), which tempted Georgescu-Roegen to state the following in 1979:

The simple fact that no enterprise is at present manufacturing collectorsonly with the aid of the energy produced by collectors is sufficient proof

that the correponding technology is not viable. Consequently, at present,all direct uses of solar radiation represent parasites of the fossil fuel tech-nology. [17]

This example of waste analysis illustrates why some economists are con-cerned about the prospect of economic growth. With the increasing worldpopulation and an anticipatedworldwide increase in average living standards,economic growth is a necessity. But given the inefficiency of technology andthe resultant drain on resources and production ofwaste, thesemay exceed theeconomic output bymore than a factor. But the finite size of our planet, and asa result the restricted capacity to supply resources and absorb emissions, mayhamper the required economic growth. And, in full support of what we wrotein Section 2, Ayres states that ‘‘there is every chance that the supply ofenvironmental services will dwindle as the demand, generated by populationand economic growth, grows exponentially.’’

Things get even worse if one looks at concerted efforts to establish thethermodynamic efficiency of various countries like Sweden, Japan, and Italy[18]. If the inefficiencies in the use of consumptive exergy toward final servicesare included, such studies confirm earlier estimates by Ayres [19] that theoverall efficiencies of advanced economies are only a few percent.

Exergy is a perfect measure for deciding to what extent matter (orradiation; see Chapter 15) is out of equilibriumwith our natural environment.The exergy of iron (Fe) is 376 kJ/mole, while that of iron oxide (Fe2O3) is 16.5kJ/mole. So iron ore, whichmay not exactly be iron oxide but amore complexcompound, is close to equilibrium with the environment, but iron is not. Norare fuels like carbon (410 kJ/mole) or methane (831 kJ/mole), and fortunately

Figure 6 The size of waste corresponding to US$500 in Germany in 1990.

Economics, Ecology, and Thermodynamics 267

we can exploit these as resources for the exergy needs of our activities. Exergycan be calculated from thermodynamic equilibrium properties. The tables inChapter 7 show, for various compounds, to what extent they are out of equi-librium with the environment. Living systems, organisms, are out of equilib-rium because of their complex composition, and due to their dynamic naturethey tend ‘‘to fall back’’ to the dead state unless food is supplied as a sourceof exergy. This can be compared to the electrical work introduced and lost ina refrigerator to keep a product out of equilibrium with the environment, notso much in composition as in temperature.

So exergy is ‘‘that part of the energy embodied in a material, whether itbe a fuel, food or other substance, that is available to perform work,’’ to becontained as in a compound (food) or to be dissipated as in a process (refrig-eration). As such it is also a measure for the quality of the energy underdiscussion. Here, engineering science offers a wonderful common measure ofresource quantity and quality that cannot be supplied by either mass orenergy. In this way economists are offered ‘‘a resource accounting frameworkcovering stocks and flows of, not only, fuels, agricultural and forest productsand other industrial materials, but also of wastes and losses.’’

This brings us to life cycle analysis (LCA), the essence of which is tocompare the consolidated inputs and outputs of a process or of a productfrom ‘‘the cradle to the grave’’ [20]. Ayres sees three advantages of using theexergy concept over energy and mass in the analysis. First, it allows theestimation of thermodynamic (exergetic) efficiency. This will tell us to whatextent the process can be improved. This improvement will have an immediateimpact on the amount of resources employed and waste and other emissionsgenerated. With an efficiency of 10%, the scope for improvement may bemuch larger than for an efficiency of, let us say, 60%. We refer to Chapter 14for further details.

The second advantage of ‘‘exergy-enhanced’’ LCA is the fact that itfacilitates comparing very different items such as chemical products, utilitiessuch as electricity and heat, and waste: comparing ‘‘apples’’ with ‘‘oranges.’’Monetary units are much less satisfactory because obviously they will be afunction of time and of other, often political, factors (‘‘the oil crisis’’) that inthe long term are not significant. Although exergy is not a panacea, it is diffi-cult to find another common measure that in quality and performance comeseven close to it. It may look inaccessible as a concept, but it is inconceivablethat an economist or politician would have more difficulties with the conceptof available work than with concepts such as inflation and deflation. And howreassuring to know that the available work concept is the co-product of twofundamental laws of science, the first and second laws of thermodynamics.

The third advantage is the possibility to accomplish year-to-yearenvironmental auditing for large firms, industries, or even nations. The cur-

Chapter 18268

rent approach is highly unsatisfactory, with a built-in incompetence tocompare flows of different nature: ‘‘apples’’ and ‘‘oranges.’’ Exergy takesaway this important imperfection.

Finally, Ayres draws our attention to the discussion of whether exergycan be considered a production factor like capital and labor. Here, engineersfeel very remote from economists because the latter seem to accept thatresources can be substituted by some combination of labor and capital andthus do not see the need for introducing exergy as a production factor. Ayresexplains that a production factor is measured based on its cost. Then exergy isclearly not a candidate because analysis of the gross national product showsthat much is spent on labor (e.g., 70%), less on capital, and little on resources.But Ayres points out that as much as labor needs capital to produce, it needsresources and so maybe labor is overvalued. Since the Industrial Revolution,labor is less and less concerned with physical labor and more so withcontributions such as information, planning, and design; thus why shouldcapital be a factor if exergy is ignored? Ayres then refers to studies thatanalyze the contributions of production factors to economic growth. Oneresult is that economic progress can for the most part (some 97%) becorrelated with energy consumption, and some economists therefore believethat exergy is the dominant production factor, the more so since closecorrelations have been found for many countries between energy consump-tion and gross national product. For engineers this is obvious: no cake withonly the cook (labor), the kitchen (capital), and without ingredients (resour-ces); no oil from only the efforts of those drilling (labor) with the help ofequipment (capital), as many dry holes have confirmed. But in the world ofeconomists, the thinking is very different, and different intelligent reasoningand argumentsmay lead to their conviction that in particular in the longer runresources are not a production factor, at least not of the same significance aslabor and capital, after all ‘‘solar energy is abundant, hence not scarce. . .’’!Economists, like the top economists of the United States, have an enormouspolitical influence that may, for example, be exerted when internationalagreements such as the Kyoto Protocol are at discussion by that country’sadministration. Therefore, it is of preponderant importance that economistsand engineers, not to forget ecologists, learn to understand each other. It willserve the interests of all members of a sustainable society and those who areworking toward achieving this.

It is clear that ‘‘eco-thermodynamics’’—although the term suggests torefer to thermodynamics’ role in ecology but was proposed by Ayres for itsapplication in economics—should deserve wide attention from economists.But as ‘‘eco-economics’’ has been coined for the complementary role ofeconomy and ecology [3], we propose that ‘‘eco-thermodynamics’’ be definedas the thermodynamics applied to ‘‘eco-economics.’’

Economics, Ecology, and Thermodynamics 269

4 FROM THERMODYNAMICS TO ECONOMICS

Earlier in this book, in Chapter 5, we discuss the maximum power that can beobtained from a heat engine driven by heat from a source at a rate of _Qin J/sec,rejecting heat to the environment at rate _Qout and producing work at a rate of_Wout. A simplified scheme is given after De Vos [21] in Fig. 7 and shows thatthe engine is assumed to run endoreversibly, by which we mean that all irre-versibilities are assumed to be concentrated in the interaction between theengine and its environment (i.e., when heat enters or leaves the engine). Underthese assumptions, a value is found for the maximum power _Wout

max:

_Wmaxout ¼ _Qin 1�

ffiffiffiffiffiffiT0

T1

r� �ð8Þ

instead of the Carnot value

_Wmaxout ¼ _Qin 1� T0

T1

� �ð9Þ

Figure 7 The endoreversible heat engine; irreversibilities are assumed to take placeonly in the engine’s exchange of heat with the environment. (From Ref. 21.)

Chapter 18270

Because of the irreversible heat exchange between the four heat reservoirs (forT0= 300K andT1= 600K), the real maximum power is found to be close toa value of 0.3 rather than the ideal value of 0.5. The maximum power is foundat an optimal flow rate _Qin

opt corresponding to an optimal set of temperaturesT2 and T3, satisfying the Carnot relation

_Wmaxout ¼ _Qopt

in 1� T3

T2

� �ð10Þ

Fig. 8 schematically gives _Wout as a function of _Qin and at the same time, thecorresponding thermodynamic efficiency g=( _Wout/ _Qin)Dhas its highest value,the Carnot value, for an infinitely slow operation of the engine at a zero heatinput rate _Qbut also at zero power output.Note that thenT2!T1 andT3!T0.The thermodynamic efficiency D is zero when _Wout is zero, but now at themaximum possible heat input rate that the engine can absorb, namely whenT2 = T3. Somewhere between these extremes the power output is at a maxi-mumvalue forwhich theheat input rate and theefficiencyareatoptimal values.

In short, this simplified thermodynamic analysis for the operation of apowerstation shows that, to a certain approximation, there is an optimal rateof heat input for which the power output is maximum. The thermal efficiencyin this mode of operation is lower than the Carnot efficiency.

Figure 8 Power output W�out (curve a) and thermodynamic efficiency D (curve b) as

a function of heat input rate Q�in for a ratio of T0/T1 = 0.5.

Economics, Ecology, and Thermodynamics 271

Next we use a similar approach to show further after De Vos [21] thatthis thermodynamic optimum is not necessarily the economic optimum. Afterall, the higher the delivered power _Wout, the faster the investments for buildingthe powerplant will be returned, but the higher the efficiency D, the better theexpenses for processing the primary fuel will be recovered. So, clearly, theeconomic optimum for the operation of the plant is in between the point formaximum power and the point for maximum efficiency, or

0 < _Qoptin;econ < _Qopt

in;therm ð11ÞDeVos assumes that the rate of running costs of the plant, _C, is made up

of two parts. One part is the capital cost, which is assumed to be proportionalto the investment and therefore proportional to the size of the plant. The otherpart consists of the fuel cost and is therefore proportional to the heat flow rate_Qin. It is then assumed that _Qmax

in is an appropriate measure for the size of theplant and thus

_C ¼ a _Qmaxin þ b _Qin ð12Þ

a and b are in economic units (ecu) per Joule, ecu/J. The quantity to bemaximized is now

p ¼_Wout

_Cð13Þ

in which p is the profit in terms of Joules produced per unit ofmoney spent. DeVos then derives a relation between Dopt and the fraction of total costs _Cincurred on fuel, the so-called fractional fuel cost f defined as

f ¼ b _Qin

a _Qmaxin þ b _Qin

ð14Þ

Table 1 gives the fractional fuel cost f for various energy sources in Belgium,De Vos’s home country. They are, of course, a function of the technologyapplied.

The result is given in Fig. 9 for an assumed ratio of T0/T1 = 0.5, that is,an ordinary powerstation. For a renewable fuel f is close to 0 and the optimalefficiency is 0.3 as opposed to the Carnot value of 0.5. For a costlynonrenewable fuel such as natural gas with f = 0.5 (i.e., 50% of all costsare spent on fuel), the optimal efficiency is 0.35, so around 15% betteralthough possible environmental costs related to the emission of waste havebeen ignored (although we should not exclude environmental costs forrenewable fuel beforehand). Fig. 10 depicts how the situation improves whenT1, the temperature of the heat source, increases. Nevertheless, the trend that

Chapter 18272

nonrenewable fuels are more favorable appears to persist, however underthe same restriction as just mentioned. By the way, this optimum, which wecall the economic optimum, is also known as the thermoeconomic optimumand the analysis with which it was obtained is known as thermoeconomic

analysis.Finally, De Vos makes the daring step from a heat engine that produces

work (as in the thermodynamic analysis) ormoney (as in the thermoeconomicanalysis) to an economic engine that produces tax revenues [22]. Fig. 11pictures the essentials of this engine. V1 and V0 are the high- and low-valuereservoirs, respectively.Goods flow upward at rates _N, fromV0 toV1, whereasmoney flows downward at rates _NV from customer to salesperson. V2 and V3

are values in exchange or prices paid by the consumer and received by thesupplier, respectively. De Vos introduces two axioms equivalent to the twolaws of thermodynamics: conservation of matter and conservation of money.

Table 1 Fractional Fuel Costf for Various Energy Sources

Fuel f

Renewable 0

Uranium 0.25Coal 0.35Gas 0.5

Source: A. De Vos, Endoreversible

thermoeconomics, Energy Conver-

sion Management 36: 1–5, 1995.

Figure 9 Optimal efficiency as a function of fractional fuel cost f for T0/T1 = 0.5.

Economics, Ecology, and Thermodynamics 273

Figure 11 The money engine. V stands for value, _N for flow rates of goods, D fortax rate, and _Wout for the rate of tax revenue.

Figure 10 Optimal efficiency as a function of the temperature ratio T0/T1.

Chapter 18274

A tax rate D is introduced according to

g ¼_Wout

_N2V3

ð15Þ

which, applying the axioms, appears to be

g ¼ V2 � V3

V3ð16Þ

Under reversible conditions, D equals the ‘‘Carnot’’ value

gC ¼V1 � V0

V0ð17Þ

Reversible conditions imply that economic activity takes place at an infinitelyslow rate; thus, _N = 0 and _Wout = 0, but D has the maximum value of DC.Applying the same techniques as above for the heat engine, an optimal rate ofgoods _Nopt can be determined for which the rate of tax revenues is at itsmaximum value. In conclusion, De Vos has shown that economics andthermodynamics, under certain assumptions, show a remarkable analogy inwhich the indirect tax revenue rate of the economic engine plays the same roleas the power produced by a heat engine!

5 ECOLOGY AND THERMODYNAMICS

With two examples we wish to illustrate the important role that thermody-namic analysis can play in investigating the quality of environmental claims.

5.1 How Green Is Green Chemistry?

In 1999 two biochemical engineers with experience in both academia and in-dustry in microbial enzymology and genetics, Gerngross and Slater [23], weredelighted with a particular executive order issued by President Clinton. Theorder insisted that researchers should work toward replacing fossil resourceswith plant material both as fuel and as rawmaterial. Bothmen had experiencein and had contributed to growing plastic in plants. They considered this atechnological breakthrough because they assumed that plant-based plasticwould be green in two ways: Use had been made of renewable resources andupon disposal they would break down, or biodegrade.

These are 2 of the 12 principles that have been defined for green

chemistry; other principles relate to a.o., health, safety, energy efficiency,use of solvents, and catalysis [24]. As we will show, such technology should

Economics, Ecology, and Thermodynamics 275

and can best be quantitatively analyzed with thermodynamic analysis and theconcepts of exergy, exergy lost, and cumulative exergy consumption, al-though for a global qualitative analysis, will probably lead to the sameconclusions through common sense. Let us follow the above researchers asthey reported their remarkable achievements and conclusions in ScientificAmerican [23].

Threemain approaches exist to replace conventional plastics with plant-derived materials. Some major industrial enterprises are, or have been active,in this field: Cargill, Dow Chemical, Monsanto, and ICI. Two ‘‘green’’plastics have drawn most attention: polylacticacid (PLA) and polyhydrox-yalkanoate (PHA). Three different routes can be distinguished. The first is theconversion of plant sugars via microorganisms into lactic acid (LA), with asubsequent chemical step for the synthesis of polylacticacid (PLA), which hasproperties similar to those of polyethylene terephthalate (PET), the plasticwell known for its use in soda bottles and clothing fibers. The second route is anice example of ‘‘the microbial factory’’ where a specific microorganismconverts the sugar directly into PHA granules that can build up to 90% of asingle cell’s mass. The third route is the most remarkable. The plastic grain,PHA, is grown directly in the plant, corn, which by proper genetic engineeringensures not only the growth of plastic grains but also that this growth does notinterfere with the production of food and takes place in the leaves and in thestem. So in addition, there is no competition for land, and one product,plastic, can be harvested after the other, corn.

This process sounds too fantastic to be true, but the process is real andexists. However, the above researchers were, quite unexpectedly, in for someunpleasant surprises, of which we will only mention the one that caused themgreatest concern to such an extent that they questioned whether it was worthcontinuing the process development. They calculated all the energy and rawmaterials required to arrive at the final product and, in their own words,‘‘discovered that this approach would consume even more fossil resourcesthan most petrochemical manufacturing routes.’’ Table 2 shows that theconventional process to manufacture polyethylene (PE) requires a total of 2.2kg fossil fuel per kg product, but 1 kg ends up in the product and 1.2 kg fossilfuel is spent on the process. In thermodynamic terms: Of 2.2 units of workmade available to the process, 1 unit is conserved and ends up as the exergy ofthe product and 1.2 units are spent in the process and dissipated. Thethermodynamic efficiency is 1/2.2 i 45%. In contrast, the plant route toproduce PHA requires 2.65 kg fossil fuel per kg product, of which nothing

ends up in the product and all is spent, dissipated in the process. The exergy inthe plastic grain stems from the solar energy source, not from the fossil fuel.The thermodynamic efficiency drops to 30%, although if it relates to the fossilenergy component it is 0%. Things are somewhat more favorable for

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microbial-made PHA and still better for the PLA process. For this lastprocess it is expected that exergy dissipation will come close to that ofpolyethylene manufacturing.

Yet there is another point of concern. If exergy dissipation for 1 kg ofPLA and 1 kg of PE is comparable, PLA seems to be preferred because itsexergy content is of solar origin. But the fossil fuel for the petrochemicalindustry is oil, whereas the fossil fuel for the agricultural industry, at least inmany American states, is coal. From Chapter 7 it is clear that for the sameamount of exergy required, the CO2 emission is at least twice that of oil. Soplant-based plastic creates a CO2 emission that is twice that for petrochemicalplastic, indeed a serious point of concern. In the meantime it has becomeobvious that the focus of attention should not be the exergy source for theexergy contained in the plastic, but the source of exergy for the exergydissipated in the process. The solution then seems to be that exergy from arenewable exergy source should pay for the dissipation, for the work lost. Oneof the surprising conclusions in this field of activities is that both emissionsand depletion of fossil resources can be abated by continuing to make plasticsfrom oil (i.e., to transfer exergy from oil to plastics) while fueling the process(i.e., paying for the exergy dissipation in the process), with renewable biomassas the fuel. Indeed, Monsanto calculated that the power that could begenerated from the corn waste after harvesting corn and PHA plastic grainswas more than sufficient to run the process. Other points of attention shouldbe that the renewable PLA and PHA are biodegradable but conventionalfossil fuel-based plastics are not. On the other hand, biodegradation ofrenewable plastics may generate undesired emissions such as CH4. PLAand PHA produced via fermentation compete with other needs for land;PHA grown in corn does not.

The researchers conclude that there is no single strategy that canovercome all environmental, technical, and economic limitations of the

Table 2 Fossil Fuel (FF) and Solar Energy (SE) Contributions to the Productionof Polyethylene (PE), Polylactic Acid (PLA), and Polyhydroxyalkanoate (PHA)in kg Fuel/kg Product

FF SEa In product Process

PE 2.2 — 1 1.2PLAb 1.2–2.0 1 1 1.2–2.0PHAb 2.39 1 1 2.39PHA 2.65 1 1 2.65

a Inefficiency of solar energy recovery not taken into account.b Via fermentation.

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various process alternatives at the same time. Biodegradability, CO2 andother emissions, and competition for land are factors to consider. Neverthe-less, it seems that using energy and raw materials from renewable sources willprovide the best solution for building a sustainable society, but it seems,again, unavoidable to lean heavily for some time on fossil fuels en route. In theshort term this will not be economically feasible; on the longer term it seems amust, as E. O. Wilson points out [2]. The challenge is to design the smoothtransition from one track to the other, in terms of both technology andeconomics.

5.2 The Renewability of Bioethanol from Corn

In 2001 three Canadian researchers published an exergetic evaluation of therenewability of a biofuel [25]. The biofuel is ethanol and is produced fromcorn at conditions prevailing in the Canadian province of Quebec. Theauthors define a resource to be fully renewable if ‘‘regeneration mechanismsexist for the resource which maintain it intact without disturbing theenvironment.’’ They recall the essence of a thermodynamic cycle, in partic-ular the thermomechanical cycle (Fig. 12), where heat from a high-temper-ature reservoir, the source, and with the help of a working fluid, produceswork, rejecting the remaining heat to a low-temperature reservoir, the sink.Usually the working fluid does not change its chemical composition,

Figure 12 Schematic representation of a thermodynamic cycle.

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although, as in thermochemical cycles, this is possible. An ecosystem maythen be considered a natural thermochemical cycle, where the sun acts as thesource, space acts as the sink, compounds confined to the hydrosphere,atmosphere, and lithosphere acting as the working fluid. This cycle generatesthe work to sustain life (Fig. 13) and, over geological times, may evenaccumulate exergy such as in the form of fossil fuels, which are considerednonrenewable because they are consumed much faster in human utilizationthan they are produced by nature. The ideal thermochemical cycle that theauthors have focused on is the natural growth of corn, the human-assistedtransformation of the corn’s glucose into ethanol, and the subsequentcombustion of ethanol back to the natural components CO2 and H2O forthe production of work.

In their analysis the authors soon realized that in practice there is adeparture from ideal behavior in the sense that nonrenewable resources suchas fossil fuel are unavoidable in carrying out this cycle (Fig. 14). Largeamounts of nonrenewable resources slip into the process for both resourceprocessing as well as waste treatment; for example, fossil fuels such as dieseland propane, fertilizers, pesticides, lime, and electricity. Although in Quebecthe electricity is from hydropower, which is a renewable resource, theassociated consumption of nonrenewable resources for the construction of

Figure 13 Schematic representation of a thermodynamic cycle in an ecosystem(ideal process).

Economics, Ecology, and Thermodynamics 279

the dam is not insignificant and has to be included. Instead of a conventionalexergetic efficiency for electricity production of about 25%, the exergeticefficiency for electricity in Quebec is close to 83%, assuming that 95% of theelectricity is generated from hydroeletric sources and 5% from fossil fuelcombustion.

Next the authors remind us of the concept of cumulative exergyconsumption, CExC, Chapter 7. For example, in our example of polythylene(PE) manufacturing in Section 5.1, we mention that the production of 1 kg ofPE requires 2.2 kg fossil fuel. Assuming as an approximation that bothproduct and fuel consist of ethylene (–CH2CH2–) segments, the product’sexergy requires an additional 1.2 times this exergy for processing, exergydissipation if you may, making the CExC 2.2 times the product’s exergy. Inthis example of ethanol production from solar exergy, CO2 andH2O via corn,by far the largest fraction of the exergy from nonrenewable resources, end upoutside the product as the exergy contained in the product originates in thesolar radiation. Table 3 summarizes the cumulative exergy consumption inMJ that equals the total exergy dissipation for the production of ethanol from1 ha of corn, that is, 56,000 MJ of chemical exergy produced.

In other words, in order to produce one unit of renewable exergy inethanol, two units of exergy are dissipated originating in nonrenewableresources. Things get worse if hydroelectricity is not available and if, forexample, coal or natural gas is used, as is not uncommon in American

Figure 14 Schematic representation of a nonideal thermodynamic cycle in anecosystem.

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agricultural states. The electricity consumption in terms of nonrenewableresources will then sharply increase, with a factor of five ormore, and the sameholds for the CO2 emission. Based on these findings, the authors conclude thatbioethanol from corn is not renewable.

Shell Global Solutions [26] plans to follow a route similar to the one thatMonsanto considers in the production of plant-based plastics: After harvest-ing, use the waste. InMonsanto’s case, the waste seems to be sufficient in massas the source for the considerable energy requirements for the production andprocessing of corn and plastic grains. In Shell’s case, waste acts as a rawmaterial for bio-ethanol and the question remains if enough of the waste is leftfor the energy requirements to originate in renewable resources, but the ligninpart of it seems to be sufficient [27].

These two examples from the world of green chemistry—the manufac-ture of chemicals and fuels from renewable resources—should clearly showhow difficult it is to eliminate or avoid nonrenewable resources and howcomfortably such processes can be analyzed with the help of thermodynamicconcepts. Ecology needs thermodynamics, albeit common sense may reachthe same conclusions in a qualitative fashion.

From these examples it also seems clear that a transition to a sustainablesociety will make use of fossil fuels. Fig. 15 summarizes what could describethe transition and what dynamics may be involved. Incremental improve-ments in eco-efficiency with conventional processes will have a small impacton sustainability. Simultaneously, development of a sustainable path willoccur, but these will not be widespread, in the short term. In the long term,however, this pathwill hold the future.Thisdual approach,whichwediscuss infurther detail in Chapter 19, clearly shows that society will remain dependenton fossil fuels in the short term, while preparing for the future.

Table 3 Cumulative Exergy Consumption inMJ for the Production of 56,000 MJ Ethanolfrom 1 ha of Corn

Corn production 27,788 MJ

Corn into ethanolDiesel 49,507Electricity 8,764

Water treatment

Electricity 25,619Total 111,678a

a Includes 34,485 MJ of electricity from hydropower.

Economics, Ecology, and Thermodynamics 281

6 CONCLUSIONS

When the reach of an economy is extended to include its interaction with theenvironment in terms of a.o. resources and emissions, economic theories andmodels need to be adapted to account for this. Lester Brown [3] uses the term‘‘eco-economy’’ to define ‘‘an environmentally sustainable economy,’’ aneconomy that ‘‘requires the principles of ecology to establish the frameworkfor the formulation of economic policy.’’ Thermodynamics, in particular thetwo main laws, appears to be one of the disciplines that should be introducedto strengthen the foundations of such an economy. When thermodynamics isapplied in this field, we propose to call this application eco-thermodynamics, aterm that has been introduced by Robert U. Ayres [11].

With the help of some examples from Alexis de Vos [21,22], we haveshown how easily thermodynamic principles can be transplanted form anengineering to an economic environment. We have also shown that thermo-

Figure 15 Biostability and hysteresis. Structural stability of chemical dynamicalsystems may display above behavior. (from Ref. 28.) The parameter E may be theresidence time in the reactor. Upon increase of E, while on the lower branch (a), this

parameter may reach a value E2, and the system jumps from branch (a) to (b). Upondecreasing E while on (b), the system may jump back to (a). For E1 < E < E2, thesystem can have more than one stable steady state, its behavior depends on its history,and the system may exhibit hysteresis. It is tempting to consider (a) the fossil branch

and (b) the renewable branch in a graph where sustainability is plotted againstenvironmental concern or time.

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dynamics is very powerful in analyzing claims on the ‘‘green’’ character ofproducts and processes. One aspect that has struck us most in eco-thermo-dynamic analysis is how difficult it seems to leave the fossil or nonrenewable‘‘track’’ and make the transition to the renewable or sustainable ‘‘track,’’ or,in terms of social change, to cross the threshold. Renewable products andprocesses (will) appear to lean heavily for a while on nonrenewable resources.Therefore, short-term values are in the way, and long-term values are too farin the future. Innovation in technology and, even more so, in ideas oninvestment is required to help us pass through the ‘‘bottleneck,’’ as E. O.Wilson [2] calls it.

It seems imperative to embark on a multidisciplinary approach towardsustainability with contributions from at least the disciplines of economics,ecology, science, and technology. It seems risky to rely solely on those whoappear to be most influential in political decisions: the economists. ‘‘Howcould they have been so wrong?’’ exclaims Robert Ayres in despair, after hehad analyzed the reasoning of American senior economists which was behindthe Bush Administration’s refusal to subscribe to the Kyoto agreement on thereduction of greenhouse gas emissions [8]. It is in nobody’s interest to dependso heavily on one single discipline, in particular when the practitioners of thisdiscipline are known to be preoccupied with short-term values.

REFERENCES

1. Webster’s New Twentieth Century Dictionary. 2d ed. Simon and Schluster,1983.

2. Wilson, E.O. The Bottleneck, feature article. Scientific American, Feb. 2002.3. Brown, L.R. Eco-economy. Building an Economy for the Earth; Earthscan:

London, 2001.

4. Ayres, R.U. Various of his publications are given below, of which we considerRef. [11] as one of the most important.

5. Costaza, R. et al. The value of the world’s ecosystem services and natural

capital. Nature May 16, 1997, 387, 253–260.6. Yoda, S., Ed.; Trilemma. Three Major Problems Threatening World Survival,

Tokyo, Japan: Central Research Institute of Electric Power Industry, 1995.7. Wackernagel, M.; Rees, W. Our Ecological Footprint, Canada: New Society

Publishers, 1996. See also the forum on this subject in Ecological Economics2000, 32, 341–394.

8. Ayres, R.U. How economists have misjudged global warming. World Watch,

12–15, Sept./Oct. 2001.9. Georgescu-Roegen, N. Myths about energy and matter. Growth and Change,

16–23, Jan. 1979.

10. Dixit, A.K.; Pindyck, R.S. Investment Under Uncertainty, Princeton University

Economics, Ecology, and Thermodynamics 283

Press: New Jersey, 1994. See also from the same authors, The Options Approachto Investment, Harvard Business Review: 105–115, May/June 1995.

11. Ayres, R.U. Eco-thermodynamics: Economics and the second law. Ecological

Economics 1998, 26, 189–209.12. The Brundtland Report, Our Common Future, The World Commission for the

Environment and Development, 1987.

13. Baumgartner, S.; de Swaan Arons, J. Necessity and inefficiency in waste gen-eration. A thermodynamic analysis. J. Ind. Ecol. 2003, 7.

14. Szargut, J.; Morris, D.R.; Steward, F.R. Exergy Analysis of Thermal, Chemical

and Metallurgical Processes; Hemisphere Publishing Corporation: New York,1988.

15. Baumgartner, S.; Department of Economics; University of Heidelberg, Ger-

many; private communication.16. Heyduk, A.F.; Nocera, D.G. Hydrogen produced from hydrohalic acid solu-

tions using a two-electron mixed-valence photocatalyst. Science 2001, 293, 1639.17. Georgescu-Roegen, N. Myths about energy and matter. Growth and Change,

16–23, Jan. 1979.18. Wall, G. Exergy conversions in Japanese society. Energy 1990, 15, 435–444.19. Ayres, R.U.; Kneese, A.V. Externalities: Economics and thermodynamics. In

Economics and Ecology: Towards Sustainable Development, Archibugi, Nij-kamp, Eds.; 1989.

20. Ayres, R.U.; Ayres, L.W.; Martinas, K. Exergy, waste accounting and life cycle

analysis. Energy 1998, 23, 355–363.21. De Vos, A. Endoreversible thermoeconomics. Energy Conversion Management

1995, 36, 1–5.

22. De Vos, A. Endoreversible thermoeconomics. Energy Conversion Management1997, 38, 311–317.

23. Gerngross, T.U.; Slater, S.C. How green are green plastics. Feature Article Sci-entific American, August 2000.

24. Anastas, P.T.; Warner, J.C. Green Chemistry, Theory and Practice; OxfordUniversity Press, 1998.

25. Berthiaume, R.; Bouchard, C.; Rosen, M.A. Exergy Int. J. 2001, 1 (4), 256–268.

26. Shell Global Solutions, Impact, Issue 3, 2002.27. Petrus, L. Project leader Biofuels. Shell Research and Technology Center Am-

sterdam (SRTCA). The Netherlands, June 2003. Private communications.

28. Nicolis, G.; Prigogine, I. Exploring Complexity; W. H. Freeman and Company:New York, 1989.

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19Future Trends

1 INTRODUCTION

The end of the Stone Age was not heralded by a sudden shortage of stones.Similarly, our society’s transformation to become sustainable will not be dueto a sudden shortage of nonrenewables. Nontraditional sources of energyare becoming increasingly popular, and large investments are being made ina sustainable future. But what will the future hold? A definite answer willonly be given once the future truly has arrived, but short of that, we canmake some predictions based on current trends and speculate about thefuture of the chemical and energy industries.

Experts seem to agree that the reserves of fossil fuels are finite, and oneday will run out. However, estimates as to when this will occur vary a greatdeal. Some people worry that the use of fossil fuels will lead to elevated levelsof the greenhouse gas carbon dioxide and that the ensuing global warmingwill change weather patterns, causing floods and droughts.

The future is by no means gloomy. On May 31, 2002, the EuropeanUnion ratified the Kyoto Protocol, and it now requires the 15 member na-tions to cut their emissions by an average of 5% over the period 2008–2012.Based on this information, it is conceivable that substitutes for fossil fuelswill be sought, thus stimulating alternative technologies.

In this chapter we try to offer a glimpse of what the future of the energyandchemical industriesmayholdand try topointout someof the technologicalhurdles that have to be overcome to reach the goal, a sustainable society. Wepoint out thatwehave not discussed nuclear power industries anddonot knowwhat role they will play in the future.

285

2 ENERGY INDUSTRIES

Currently, a large proportion of energy comes from nonrenewable fossilfuels (see Chapter 9). Possible viable alternatives are wind and solar energy.In certain cases, for example, Iceland, geothermal energy is viable as well.It is conceivable that large offshore wind farms such as those built off theshore of Denmark may become more commonplace worldwide. The oilindustry has considerable experience in operating in hostile offshore envi-ronments. Its technological expertise could prove vital in large-scale offshoreprojects.

The role of decentralized energy generation is likely to increase in thefuture. According to the California Energy Commission, the averageCalifornian household requires 6,500 kWh annually, which is less than thenational average of 10,400 kWh. Now, commercially available photovoltaicpower cells have typical efficiencies of around 14% and can supply about140 W/m2. This means that 10,400 � 1000/(140 � 8 � 365) = 25 m2 of solarpanel area are needed per household in the United States for 8 hours ofdaylight. Since the energy requirements per household are generally lessoutside the United States, this number is likely to be lower in other parts ofthe world. Note that the new generation of photovoltaic solar panels canfunction in low light, such as overcast conditions. The implication of this isthat using a significant part of the roof area for photovoltaics can take careof a great deal, if not all, of the electricity requirements of an averagehousehold. It is therefore conceivable that, in the future, decentralizedenergy production will supplement large-scale centralized energy produc-tion. For example, solar panels mounted on houses will supply a certainamount of electricity. If this supply exceeds the household’s demand at thattime, the electricity can be sold back to the electricity supplier. Conversely, ifthe demand is higher than the supply of the solar panels, electricity can bebought from the supplier [1]. Similarly, local waste-treatment facilities couldgenerate electricity to serve the local population (see Chapter 16). Aninteresting point is that recently researchers at the University of Californiaat Berkeley have made significant progress in producing cheap plastic solarcells. Till date, clean rooms, and complex manufacturing procedures arenecessary to produce the semiconductors, whereas the researchers onlyrequire a laboratory flask at room temperature [2]. Though their develop-ment is still in their infancy, such solar cells may prove useful in the future.

Solar energy may prove to be the ultimate renewable energy source,but currently we depend heavily on hydrocarbon fuels. These hydrocarbonfuels, as the name well suggests, consist of hydrogen and carbon, and thehydrogen–carbon ratio of these has interesting consequences. For very smallvalues of this ratio, carbon dominates and the hydrocarbon is essentially

Chapter 19286

solid at room temperature and pressure; coal is a good example. At highervalues, the hydrocarbon becomes liquid (e.g., gasoline), which is a mixtureof hydrocarbons, and even higher values, a gas (e.g., methane). As the ratioincreases, the amount of CO2 emitted per unit exergy decreases. Now whathappens when the hydrogen:carbon ratio tends to infinity? In that case, weend up with hydrogen, which is no longer a hydrocarbon and has no CO2

emissions per unit exergy.Hydrogen is likely to play an important role in the future. On January

28, 2003, the Bush Administration pledged $1.2 billion in funding forhydrogen fuel research over five years [3]. The European Union has com-mitted up to $2 billion for research into hydrogen and other renewableenergy sources, said Spencer Abraham, U.S. Secretary of Energy at the In-ternational Energy Agency meeting in Paris [4].

Proponents of hydrogen frequently make the statement that hydrogenis the most abundant element in the universe. This statement, while factuallycorrect, has to be examined. Terrestrial hydrogen is present in largequantities such as H2O, or water. Liberation of this hydrogen by electrolysisrequires electricity, which today is generated in large part by fossil fuels.Moreover, present-day hydrogen production occurs mainly by the reform-ing of fossil fuels.

It seems that three challenges have to be met in order to have wide-spread use of hydrogen as a sustainable transportation fuel. The first chal-lenge is to produce hydrogen in a sustainable fashion. This can be achievedby using renewable electricity in the electrolysis of water. Examples includeusing solar, wind, geothermal energy, or nuclear energy, as some have sug-gested. The challenges regarding spent-fuel processing in the nuclear optionstill remain, though. Other examples are gasification of biomass and muni-cipal waste.

The second challenge is storage of hydrogen, and the third is trans-portation of hydrogen, which are inseparable. The current infrastructure isdesigned for liquid fuels and gaseous fuels at moderate pressures, for ex-ample, natural gas in Western Europe is transported at pressures at theorder of 70 bar. To liquefy hydrogen, very high pressures and low temper-atures are necessary, making it a nonviable option* or at best a very expen-sive one. Currently, researchers are looking into developing a hydrogeninfrastructure that delivers hydrogen gas at high pressures, at the order of250 bar or higher (e.g., [5]).

Various options are considered such as direct hydrogen production atretail stations by reforming, electrolysis using solar or wind energy, and so

*The critical temperature of hydrogen is 33 K, whereas the critical pressure is 12.4 atm.

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forth. When performing these analyses for transportation, the results arefrequently compared to equivalents of gasoline and cost per mile. For ex-ample, a typical passenger car today has a fuel economy of about 35 miles/gal. Gasoline, excluding taxes, costs about $1/gal. Incidentally, thisnumber is fairly constant throughout the world, and the discrepancy inworldwide gasoline prices is due to taxes. This equates to a price of $1/35miles = 2.9¢ per mile. Hydrogen-powered fuel cell vehicles are expected tohave much higher fuel economies, at the order of 100-miles/gal. gasolineequivalent [5]. Here, one gallon gasoline equivalent corresponds to 130.8MJ (HHV). The delivery cost of hydrogen produced using solar energyin southern California is about $22 � $30/GJ. The cost is therefore $22 �0.1308 – $30 � 0.1308 = $2:87–$3.92/gal. The correct metric in this case,however, is the cost per mile, which is $2.87/100 – $3.92/100 = 2.9–3.9¢.The cost ranges between 2.9¢–3.9¢/mile. For hydrogen produced fromnatural gas it is about twice as low, or 1.4¢–2.0¢/mile. The orders of mag-nitude of the cost per mile driven for a standard gasoline-powered car anda hydrogen-powered car are about the same. This very simple calculation,subject to the assumptions of fuel economy and cost and not taking intoaccount the energy expended in building the cars and solar panels, etc.,indicates that there is no direct ‘‘red light’’ to stop the use of hydrogen.For more details, the interested reader is referred to the literature (e.g.,[5]).

President Bush’s hydrogen initiative will try to address some of thehurdles facing widespread use of hydrogen [6], which include lowering thecost of hydrogen, creating effective hydrogen storage, and creating moreaffordable fuel cells that use the hydrogen.

Joan Ogden, a research scientist at the Princeton EnvironmentalInstitute and a longtime analyst of alternative fuels, testified before theHouse Committee on Science as part of a hearing on ‘‘The Path to a Hy-drogen Economy’’ on March 5, 2003. The hearing was the first formal ef-fort by Congress to respond to Bush’s hydrogen initiative. According toOgden, hydrogen fuel cells, although they are long-term, potentially havea very high payoff. Furthermore, this technology deserves significant gov-ernment support now. This will act as insurance, if nothing else, that theywill be ready in 15 or 20 years if we want to deploy them on a very wide basis[7].

It is likely to take about 40 to 50 years according to Ogden and otherPrinceton researchers before hydrogen replaces fossil fuels. At least 10 yearsare necessary, according to experts, before hydrogen finds widespread use incars or industry. As such, it is useful to take stock of where we are now, andwhere we want to go. Currently, we are in the so-called fossil fuel age. Ourfinal destination is a sustainable age. This sustainable age could well be the

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‘‘solar age.’’ Here, we use the term ‘‘solar’’ loosely, since renewables such assolar energy, wind, and biomass all find their origin in the sun. Even hydro-electric energy depends on the flow of rivers, which are fed by precipitationthat in turn is partly attributable to the sun driving the water cycle. In thetransition period between the fossil fuel and solar ages, combinations ofrenewable and nonrenewables will become popular, since an overnighttransformation of society is not possible. As such, natural gas will becomeincreasingly important as its high hydrogen-to-carbon ratio makes it a goodsource of hydrogen, and it has low CO2 emissions per unit exergy.

Research is presently being conducted at the Los Alamos NationalLaboratories [8] among others on so-called zero emission powerplants usingcoal. The concept here is to convert water and coal into hydrogen, which inturn is converted into electricity using fuel cells. The hydrogen is producedfrom the water and coal through an intermediate calcium oxide (CaO)conversion to calcium carbonate (CaCO3). In a subsequent step, the calciumcarbonate is converted back into calcium oxide and a stream of pure CO2.The carbon dioxide is then disposed of through mineral carbonation. It isclear that this technology can be adapted to other fossil fuels or biomass.Technologies such as this could be useful in the transition state between thefossil fuel age and the sustainable age and perhaps, if using biomass, in thesustainable age. Therefore, hydrogen production from fossil fuels willundoubtedly continue, albeit perhaps with sequestration of the carbondioxide as mentioned earlier.

It remains an open question how much more efficient fuel cells will bethan finely tuned internal combustion engines. A theoretical efficiency onpaper does not necessarily mean it can be observed in practice [7]. For thisreason, experts in the science of combustion believe that it is important toconsider uses of hydrogen other than in fuel cells. One possibility is to burnit like a conventional fuel, rather than converting it chemically to electricity.Conventional internal combustion engines might be modified readily toburn hydrogen, or a mix of hydrogen and gasoline [7]. Compared to fuelcells, this technology is much easier to implement.

Mixing hydrogen and fossil fuels could reduce some of the dangersassociated with pure hydrogen, which is explosive and burns with an invi-sible flame. Public perception of hydrogen fuel suffers from a fear of catas-trophic explosions—‘‘the Hindenburg syndrome’’—but the dangers couldbe managed with the use of strong storage tanks and good sensors to detectleaks [7].

In 1999 Shell Hydrogen was established as a global business divisionof the Royal/Dutch Shell Group. A large multinational company such asShell, which is also one of the largest integrated oil companies, deems itnecessary to invest significantly in renewables, and such an effort may prove

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useful in the future. On April 24, 2003, Shell Hydrogen opened the first Shellbranded retail hydrogen station in Reykjavik, Iceland. The hydrogen retailstation is located next to a regular Shell station and will serve to providehydrogen to three DaimlerChrysler fuel cell buses that drive on Reykjavik’sstreets on a commercial basis. Iceland produces the hydrogen electrolyti-cally, while the electricity in Iceland is generated hydroelectrically and geo-thermally and therefore constitutes a good example of sustainable energyproduction. Currently, Shell Hydrogen is involved in other pilot studiesthroughout the world with hydrogen retail stations.

On November 20, 2002, Stanford University launched the GlobalClimate and Energy Project (G-CEP), which is a multimillion-dollar alliancebetween industry and academia to develop innovative technologies that willmeet the world’s growing energy needs while protecting the environmentalhealth of the planet [9]. Some of the industrial partners include ExxonMobil,General Electric, and Schlumberger. The sponsors expect to contribute $225million over the next 10 years. These developments may be indicating that ashift in priorities in society is occurring.

In August 2001, researchers at MIT managed to produce hydrogenphotocatalytically from water. While not as complete and efficient as photo-synthesis, this system comes close to the ideal use of a molecular catalyst aspart of a homogeneous reaction, for which scientists have been searchingfor more than three decades. Even though the process is still in its infancy,improvements of the process could some day allow the energy of the sun tobe used to directly convert water into hydrogen and provide a sustainablesource of energy fuel [10,11].

One of the trends visible today is to use hydrocarbons as the storagemedium for hydrogen and use on-board reforming to create the hydrogenon site. Storage could be possible by physical dissolution in carbon-richmaterials or chemically bonded. This circumvents many of the problems as-sociated with the storage and transportation of hydrogen, since existingfacilities can be used. The carbon in the hydrocarbon could be obtained byrenewable means by gasification of biomass to obtain synthesis gas followedby Fischer–Tropsch synthesis of hydrocarbons. Another, perhaps less cost-effective, option would involve the direct decomposition of carbon dioxideinto oxygen and carbon monoxide, followed by Fischer–Tropsch synthesis.Unfortunately, the decomposition reaction is thermodynamically favorableonly at very high temperatures. It seems that nature is more efficient at roomtemperature to fixate the carbon!

In any case, a storage strategy that involves hydrocarbons as opposedto pure hydrogen may be a useful technology for the transition between thefossil fuel age and the sustainable age and could be implemented withoutmaking any significant changes to the infrastructure.

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3 CHEMICAL INDUSTRIES

Today, much of the chemical industry uses nonrenewable fossil fuels as theraw material. In the future, it is likely that Fischer–Tropsch synthesis willyield many chemicals from renewable hydrogen and carbon, which couldcome from biomass or even municipal waste. Currently, the proportion offossil fuel actually used as fuel is much larger than that used as feedstock forthe chemical industry. In the future, however, ‘‘fossil fuels’’ will no longer beused for their value as fuel, but could conceivably be used for theirinteresting chemical properties. It is interesting to note that currently about90% of the fossil fuels expended in chemicals production is used in drivingthe process and does not end up in the product on an exergy basis.

Needless to say, society is essentially an inert giant, which needs someprodding to change. This change will, of course, require monetary resources.When evaluating the cost of changing, one should not forget that the changemay not benefit our generation, but is intended for the generations thatcome after us, and, hence, the use of standard economic indicators may notbe useful. As Jeroen van der Veer, President of the Royal Dutch PetroleumCompany and Vice-Chairman of the Committee of Managing Directors ofthe Royal/Dutch Shell Group, points out in his speech given at the unveilingof the first hydrogen retail station in Reykjavik: ‘‘. . . competitiveness mustcome from the added benefits produced in cleaner air, lower CO2 emissionsand improved energy supply security.’’ To this he also adds, ‘‘that is why weneed a twin track approach that utilizes fuel reformer technology to producehydrogen from the world’s existing hydrocarbons industry, while at thesame time supporting the development of an entirely new and commercialhydrogen infrastructure, where commercially and politically feasible.’’Standard economic indicators, therefore, may not be appropriate whenevaluating the feasibility of sustainable chemical or energy projects. Forexample, it has been shown [12] that to build a photovoltaic solar energyplant that lasts about 30 years, approximately one third of the exergy pro-duced over those years is actually necessary to build the plant. This con-trasts starkly with the one twentieth needed for energy plants based on fossilfuels.

Traditionally, investment decisions have been guided by tools such asthe net present value (NPV), which takes into account the time value ofmoney and is formally defined as the difference between the present value ofcash inflows and cash outflows using a certain annual discount rate. TheNPV is easy to calculate, but, as Dixit and Pyndick have pointed out, it isfrequently wrong [13,14] since the NPV analysis is based on faulty assump-tions. Either the investment is reversible and can be undone when conditionschange, or if it cannot be changed, the investment has to be done now-or-

Future Trends 291

never. This binary approach is not always applicable, and the ability to delayprofoundly affects the investment decision. A richer framework is necessaryto account for the gray area between the binary possibilities.

Instead of assuming either that investments are reversible or that theycannot be delayed, recent research on investment stresses the fact thatcompanies have opportunities to investment and that they must decide howto exploit those opportunities most effectively, analogous to financialoptions. A company with an opportunity to invest is holding somethingakin to a financial call option. When it decides to invest, the call option isexercised.

When a company immediately makes an investment decision, the op-tion is effectively killed, as the possibility to wait for new information iswaived. An option value has important implications for managers as theythink about their investment decisions. For example, a standard analysismay indicate that an investment is economical right now, but it is oftenhighly desirable to delay an investment decision and wait for more infor-mation about market conditions. On the other hand, situations may arise inwhich uncertainty over future market conditions should call for a companyto accelerate certain investments [13,14]. A good example is investment in Rand D, since it can lead to patents, which gives the company freedom tooperate in future, if it chooses to do so.

Many managers already seem to understand that the NPV rule is toosimplistic and that there is value in waiting for more information. In fact,many managers often require that an NPV be more than merely positive. Inmany cases, they insist that it be positive even when it is calculated using adiscount rate that is much higher than their company’s cost of capital bysetting a hurdle rate. Disinvestment is guided by similar rules. Companies arewilling to sometimes take a loss and wait until demand improves to maintaintheir foothold in the market, rather than close their operations and effectivelydisinvest. Applying the traditional NPV analysis to funding of long-termresearch and development projects can also lead to decisions that halt R &D.Research and development gives a company future possibilities, but its valueis hard to quantify. High-risk projects may revolutionize the business, butmay be very high-cost and long-term. Low-risk projects may only incremen-tally improve the business. For example, directed research at slightly improv-ing the yield of a catalyst will only incrementally change the business and beprofitable, but changing the process in its entirety may be high-risk and couldrevolutionize the business by doubling the yield or eliminating variousintermediate process steps.

Patenting an invention in a sense creates an option for the company byallowing it to gauge the market potential and giving that company the rightto pursue a particular investment.

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The acquisition of oil fields is also a good example of decisions wheredelay is factored in. A company that buys an oil field may develop itimmediately or later, depending on market conditions. The company iskeeping its options open. Investments in sustainable technology are muchthe same. These investment decisions may or may not have favorable NPVs,but when market conditions change, it could be a different story. Invest-ments in solar energy, for example, are likely to pay off in the long term. Assuch, these investments are options to an infinite energy source in the future,and to cash flow. At present, conventional fossil energy sources are lessexpensive, and as such one could argue that investments should be made inthe latter rather than the former. But when fossil energy sources become lessabundant, the political or environmental situation is such that the prices goup, so the picture for solar will be much more favorable. That is to say, inthe short term, the NPV would give a negative indicator for solar energy,whereas in the long term, when fossil fuels are scarce, a positive indicator.However, it is important to realize that as sustainable technology develop-ment is a process fraught with technical challenges and its payout is in thelong term, the option to use this technology should be pursued now byappropriate research. Changes in economic analysis will therefore also beinstrumental in analyzing sustainable technology options.

In order to make a transition to a sustainable society, initially fossilfuels will play an important role. Fossil fuels will be expended in buildingthe first sustainable chemical and energy plants. In the short term, hybridtechnologies may be popular, which mark the transition from the ‘‘fossilperiod’’ to the ‘‘solar period,’’ which could be the final sustainable society.Undoubtedly, natural gas will become important in the short term.

We are currently in the fossil fuel age, and our final destination is thesustainable age. Once fossil fuels run out, the fossil fuel age will have to end,and this allows us to estimate the time we have left to make the transition tothe sustainable age. We assume that the demand for fossil fuels does notincrease and that new reserves are not found. This is a very important as-sumption in obtaining this estimate, since the population will grow and, assuch, with the same energy demands per capita, the demand will grow aswell. Furthermore, supply may increase by the discovery of new reserves.Estimates of reserves are difficult to develop, and various sources give dif-ferent data. We will therefore take the estimate in an order-of-magnitudefashion. The following worldwide statistics are available from the EnergyInformation Agency [15]:

Estimated recoverable coal [16]—1,083 billion tonsCrude oil reserves [17]—1,212 billion barrelsNatural gas reserves [18]—5,919 trillion ft3

Future Trends 293

Coal consumption [16]—5.26 billion tons/yearCrude oil consumption [19,20]–77.43 million barrels/dayNatural gas consumption [16]—90 trillion ft3/year

To obtain the number of years left, we simply divide the reserves by theconsumption:

Coal—206 yearsCrude oil—43 yearsNatural gas—65 years

We note in passing that the consumption of crude oil, natural gas, andcoal is expected to increase at 1.8%, 2.8%, and 1.5%, respectively [16]. Thesimple calculation indicates that in about 50 years, the age of fossil fuels willbegin to end due to the depletion of crude oil. The fossil fuel age will have toend when the coal reserves run out in about two centuries. This gives us atleast 50 years and at most 200 years to make the transition to the sustainableage.* In the next 20 to 30 years, however, fossil fuels will play an importantrole, as projections of the International Energy Agency in the 2003 EnergyOutlook indicate.

4 CONCLUDING REMARKS

The end of the Stone Age did not come because man ran out of stones. Butif man runs out of stones, then man must be ready to leave the Stone Age.Similarly, the reserves of fossil fuels such as natural gas, crude oil, tar sands,and coal are expected to last some time, but once that century has passed,the alternative options should be ready to go. It is probably best not to waituntil there is a real shortage.

Increasing the efficiency of processes will be of the utmost importancein the transition period, as well as in the solar age since high-efficiency pro-cesses will allow for more to be done with less. For example, it is attractiveto use only 1 solar panel rather than 10 to get a certain task done. Efficientuse of resources will therefore remain important. Undoubtedly, a new typeof economics will arise that can accurately quantify and analyze projectsleading to sustainable development and accurately inform the consumer ofthe costs as well.

Some scientists claim that as there is no conclusive proof of globalwarming due to anthropogenic CO2 emissions, and, as such, there is no need

*These estimates are subject to the assumptions made earlier.

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to pursue sustainable technology. However, sustainable technology is notjust about global warming. Carbon dioxide is a greenhouse gas, and levels ofthis gas will rise if fossil fuels are combusted. At best we do not know whatwill happen, but at worst it could contribute to global warming. The cruxof the matter is that fossil fuels are not renewable, and one day they willbe depleted. Sustainability is about preventing such a scenario and, amongothers, about closing the various elemental cycles so that material and energyresources remain available for future generations and so that quality of life ofthe latter is not degraded.

In our journey from the fossil age to the sustainable age we will enterthe transition period, where conventional technology will exist side by sidewith sustainable technology. Hybrid technologywill also become increasinglymore popular. The transition period will most certainly make use of conven-tional fossil fuel-based processes since this is inevitable. However, when in thistransition period, it is important to realize that the path may be hard, but thefinal destination is well worth it. In any case, many challenges await society,and how well we face these challenges will determine our future.

REFERENCES

1. Energy Information Administration 1999 data.2. Huynh, W.U.; Dittmer, J.J.; Alivisatos, A.P. Hybrid nanorod-polymer solar

cells. Science 2002, 295 (5564), 2425–2427.3. White House Press Release, Jan. 28, 2003, http://www.whitehouse.gov/news/

releases/2003/01/20030128-25.html.

4. Associated Press, April 28, 2003.5. Ogden, J.M. Developing an infrastructure for hydrogen vehicles: A southern

California case study. Int. J. Hydrogen Energy 1999, 24, 709–730.

6. White House Press Release, Feb. 6, 2003,http://www.whitehouse.gov/news/releases/2003/02/20030206-2.html.

7. Princeton Weekly Bulletin, March 31, 2003, 92(21), http://www.princeton.edu/pr/pwb/03/0331/1b.shtml.

8. http://www.lanl.gov/energy/est/zec/index.html.9. Stanford Report, Nov. 21, 2002.10. MIT News Release, Aug. 31, 2001, http://web.mit.edu/newsoffice/nr/2001/

nocera.html.11. Heyduk, A.F.; Nocera, D.G.Hydrogen produced fromhydrohalic acid solutions

using a two-electron mixed-valence photocatalyst. Science 2001, 293, 1639.

12. Yoda, S. Trilemma, Central Research Institute of Electric Power Industry;Tokyo, Japan, 1995.

13. Dixit, A.K.; Pindyck, R.S. The options approach to capital investment. Har-

vard Business Review, May–June 1995.

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14. Dixit, A.K.; Pindyck, R.S. Investment Under Uncertainty; Princeton UniversityPress: New Jersey, 1994.

15. http://www.eia.doe.gov.

16. International Energy Outlook 2003, Report #: DOE/EIA-0484, 2003.17. Oil and Gas Journal 100: 52, Dec. 23, 2002.18. World Oil 223: 8, Aug. 2002.

19. http://www.eia.doe.gov/emeu/international/petroleu.html#IntlConsumption.20. http://www.eia.doe.gov/emeu/ipsr/t17.xls.

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Index

Abundance factor, 191Advancement, degree of, 36

Affinity, 36, 42Age

fossil, 282, 293

solar, 282Anergy, 24, 184Anthropological view of sustainability,

177Applications, 83Availability, 61

Baehr, 184Bed, fixed or moving, 106Bed, fluidized, 107

Biocrude, 241Bioethanol, 240, 278Biogas, 239

Biomassconversion, 231gasification, 239upgrading, 239

Boltzmann, 11Brundtland report, 176

Carnot, 24, 52, 110, 115Clausius, 12Coal combustion, 106Cogeneration, 69, 120

Combined cycle, 102, 120Combustion, 93

Component, reference, 75Composition, 13

Compressor, efficiency of, 87Conjugated flow, 38Conversion, chemical, 147

Coupling, 38

Driving force, 27, 29, 34, 155Dissipation, 53

Distillation, 124

Ecological deficit, 187

Ecological footprint, 186Ecological view of sustainable

development, 177Ecology, 257

Economic analysis and value, 261Economics, 257Economic system, 180, 260

Economic viability, 258Eco-thermodynamics, 263Efficiency, 20, 66, 109, 115, 117, 121,

136, 155, 197, 207, 221Electric power generation, 100Elemental cycle, 232

Endoreversible thermodynamics, 50,53, 270

Energy, 23conversion, 97

outlook, 99Enthalpy, 8

297

Entropy, 8generation, 29, 33, 53

Environment, 7, 8, 15, 16, 35, 198,

262compatibility, 198damage, quantification, 262

Equilibrium, 8, 15, 16, 35thermodynamics, 33

Equipartitioning, 55

Exergy, 24, 59, 73, 77, 80, 117Expansion, 83Extruder, 151, 161

Finite time, finite size

thermodynamics, 54First law, 9Flow sheet, 140

Fractional fuel cost, 272Freezing water, 85Future

of chemical industry, 291

of energy industry, 286

Grassmann diagram, 2, 28, 154, 159,204

Gas combustion, 106

Geothermal energy, 105Global overshoot, 187Goal and scope definition, 168

Gouy, 28Green chemistry, 247Greenhouse effect, 219, 295

Heat, 9

Heat exchanger, 25, 56Heat pump, 126, 161Hilsch–Ranque tube, 91

Hydrogen economy, 287

Impact assessment, 168, 171Inventory analysis, 168, 170

Investment decision, 291Irreversible thermodynamics, 37

Joint production, 210Joule, quality of the, 66

Landfill, 240

Life cycleanalysis, 167, 268assessment, 167

Light dark reaction, 227Linear law, 40Losses, 155, 159Lost work (see Work, lost)

Magic triangle, 3, 45Manure, 16

Materials, 251Maximum power, 51, 271McCabe–Thiele diagram, 131Merkel, Angela, 178

Metabolic society, 179Methane, 111Mixer, static, 157

Mixing, 15Model, 20Money engine, 274

Muser engine, 223

National net welfare, 262Net present value, 291

Nonequilibrium thermodynamics, 33Nuclear reactor, 103

Optimization, thermodynamic, 56

Oxidation, 111

Phenomenological coefficient, 37Photosynthesis, 179, 226

Photothermal conversion, 222Photovoltaic energy conversion, 224

Index298

Planck spectrum, 216Polyethylene, 147, 149

processes, 149

Powerstation, 52Pressure, 8Probability, 11, 12

Problem, thermodynamic, 18Process, 44, 49, 156, 160, 203

improvement, 156, 160

industry, 203spontaneous, 44

Propane–propylene separation, 124

Propertiesextensive, 8intensive, 8

Pyrolysis, 238

Quality, 31, 68, 209

Rankine cycle, 101

Reduction of lost work, 47Reflux ratio, minimum, 136Renewable, 231 (see also Sustainable)

Reservoir, 110Resource depletion time, 191

Second law, 11

Separation, 92, 123

Sky temperature, 223Solar power, 105, 175, 189, 215Solar radiation, 215

Solar society, 182Steam cycle, 101, 118Stefan–Boltzmann engine, 220

Stodola, 28Sustainability, 147, 178, 199, 203, 210,

248

analysis, 188Sustainable development, 175, 176Sustainable resource parameter, 190,

193System, 7

Theocratic view of sustainability, 176

Trilemma, 176, 184Turbine, 101, 110, 116, 156Twister tube, 91

Vortex tube, 91

Waste generation, 234, 265Work, lost, 23, 29, 38, 43, 139, 203, 205Wind power, 105, 219

Yoda, 184

Index 299